Why Chemical Reactions Happen 9780199249732, 0199249733

Citation preview

why

chemical

reactions happen :

James Keeler Peter Wothers

Why chemical reactions happen

Why chemical reactions happen James

Keeler

Lecturer in the Department of Chemistry and Fellow of Selwyn College, Cambridge

and Peter Wothers Teaching Fellow in the Department of Chemistry and Fellow of St Catharine’s College, Cambridge

OXFORD UNIVERSITY

PRESS

Great Clarendon Street, Oxford 0x2 6DP Oxford University Press is a department of the Universiay of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford

New York

Auckland Cape Town Dares Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © James Keeler and Peter Wothers 2003 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2003 Reprinted 2004 (with corrections), 2005, 2006 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available ISBN 13: 978-0-19-924973-2 ISBN 10: 0-19-924973-3 5 79108 6 Typeset by the authors Printed in Great Britain on acid-free paper by Antony Rowe Ltd, Chippenham, Wiltshire

Acknowledgements

We

are grateful to Michael Rodgers, then commissioning editor for science

texts, for being so enthusiastic about our original proposal for this book and for being responsible for its adoption by OUP. Michael has since moved on to higher things, leaving us in the capable hands of Jonathan Crowe, John Grandidge, Miranda Vernon and Mike Nugent, who have been very helpful through-

out the writing and production process — we are most grateful to them for their assistance. James Brimlow and John Kirkpatrick were kind enough to read and comment on the final draft; we are very grateful to them for their suggestions

and corrections.

It is something of a cliché to offer thanks to our students for what they have taught us. However, be it a cliché or not, it is true that having to think about, explain and re-explain this material over a number of years has improved our own understanding and, we hope, the clarity of our explanations. So in a very real sense we are indeed grateful to the many students we have had the privilege to teach.

JK wishes to thank Prof. A. J. Shaka and his colleagues in the Department of Chemistry, University of California Irvine, for being excellent hosts during

a three-month sabbatical which made it possible for a great deal of progress to be made on the text. He also wishes to thank Prof. Jeremy Sanders for his invaluable advice, support and encouragement. PW wishes to thank Del Jones for his support and encouragement during the production of this book. This book has been typeset by the authors using I4TRxX, in the particular

implementation provided by MiK TEX (www.miktex.org); we are grateful to the many people who have been involved in the implementation of this type-

setting system and who have made it free for others to use. The text is set in Times with mathematical extensions provided by Y&Y Inc., (Concord, MA).

Most of the diagrams were prepared using Adobe Illustrator (Adobe Systems Inc., San Jose, CA) or Mathematica (Wolfram Research Inc., Champaign, IL), and chemical structures were drawn using ChemDraw (CambridgeSoft Corp., Cambridge, MA). Molecular orbital calculations were made using HyperChem (HyperCube Inc., Gainesville, FL). Our intention is to maintain some pages on the web which will contain

some additional material in the form of appendices, downloadable versions of

many of the diagrams and corrections to the text. The address is

www.oup.com/uk/best.textbooks/chemistry/keeler. Finally, we hope that you enjoy reading this book and that it helps in your

understanding and exploration of the fascinating world of chemistry. How re-

actions happen, and why they happen, is the most fundamental question in chemistry — we hope that you find some answers here! Cambridge, February 2003.

TO OUR AND

OUR

PARENTS TEACHERS

Contents

1

What this book is about and who should read it

What makes a reaction go? 2.1 Energy changes 2.2 Entropy and the Second Law of Thermodynamics 2.3 Entropy and heat 2.4 Role of temperature 2.5 Exothermic and endothermic reactions

2.6 2.7 2.8 2.9

3

How do we know all this is true?

The Second Law and Gibbs energy

Gibbs energy in reactions and the position of equilibrium

Where does the energy come from?

Ionic interactions

3.1 3.2 3.3 3.4 3.5

Ionic solids Electrostatic interactions Estimating lattice energies

Applications

Ionic or covalent?

Electrons in atoms

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5

Atomic energy levels

Photoelectron spectroscopy Quantum mechanics

Representing orbitals Radial distribution functions Hydrogen orbitals Atoms with more than one electron Orbital energies Electronegativity

Electrons in simple molecules

5.1 5.2 5.3 5.4 5.5 5.6

The energy curve for a diatomic

Molecular orbitals for H2

Symmetry labels

General rules for forming molecular orbitals Molecular orbitals for homonuclear diatomics Heteronuclear diatomics

vil

6

Electrons in larger molecules Two-centre, two-electron bonds 6.1 . Hybrid atomic orbitals 6.2 6.3 6.4

6.5 6.6

7

9

Reconciling the delocalized and hybrid atomic orbital approaches Orbital energies: identifying the HOMO and LUMO

Reactions

7.1. 7.2. 7.3.

The formation of Hz from Ht and H— Formation of lithium borohydride Nucleophilic addition to carbonyl

7.6

Nucleophilic attack on acyl chlorides

7.4 7.5 8

Using hybrid atomic orbitals to describe diatomics Simple organic molecules

Nucleophilic attack on C=C Nucleophilic substitution

80 81 83

88 89

93 95

97

97 98 102

106 107

110

Equilibrium

8.1 8.2

The approach to equilibrium The equilibrium between two species

113

8.3. 8.4 8.5

General chemical equilibrium Influencing the position of equilibrium Equilibrium and rates of reaction

118 122 130

113 114

Rates of reaction

131

9.1 9.2 9.3.

What determines how fast a reaction goes? Why is there an energy barrier? Rate laws

131 133 135

Elementary and complex reactions Intermediates and the rate-determining step

139 141

148

9.4

The Arrhenius equation

9.7 9.8

Reversible reactions Pre-equilibrium

9.9

The apparent activation energy

9.5 9.6

9.10 Looking ahead

10 Bonding in extended systems — conjugation 10.1 Fourp orbitals in a row 10.2

Three p orbitals in a row

10.3 Chemical consequences — reactions of carbonyl compounds 10.4 Stabilization of negative charge by conjugation

11 Substitution and elimination reactions 11.1 11.2 11.3.

Nucleophilic substitution revisited — Sj 1 and Sn2 The stabilization of positive charge Elimination reactions

11.4 Addition reactions — elimination in reverse 11.5 E2 elimination

Vili

137 143 145

150 151 153 157

163 168

172 172 174 180

183 185

12 The effects of the solvent

12.1 12.2 12.3 12.4 12.5

Different types of solvent The solvation of ions Solubilities of salts in water Acid strengths and the role of the solvent How the solvent affects the rate of reaction

13 Leaving groups

190 194 197 202 207 210

13.1

Energy profiles and leaving groups

211

13.3

Leaving groups and pK,

215

13.2 Leaving group ability

14

189

213

Competing reactions 14.1 Reactions of carbonyls with hydroxide 14.2 Reactions of enolates 14.3 Unsymmetrical enolates

216 216 221 225

14.5

233

14.4 Substitution versus elimination revisited So why do chemical reactions happen?

Index

228 234

iX

ay

1

What this book is about and who should read it

When

we first come across chemical reactions they are presented to us as

‘things that happen’ — this book is about why and how chemical reactions hap-

pen. The ideas and concepts presented here will give you a set of tools with

which you can begin to understand and make sense of the vast range of chemical reactions which have been studied. Let’s look at some examples of the kinds of things we are going to be talking about. e In solution Ag* ions and Cl7 ions react together to give a precipitate of solid AgCl:

Ag* (aq) + Cl (aq) —> AgCl(s);

on the other hand Agt and NO, solution. Why?

do not form a precipitate but remain in

e Acyl chlorides react readily with water to give carboxylic acids:

I

+

Cc

_

H2O

2

+

UC

HCl

whereas amides are completely unreactive to water; O

I

+

20

Sc

+

no reaction

Why?

e In solution 2-bromo-2-methylpropane can form the positively charged ion (CH3)3C*, but bromomethane cannot form CH}:

H3C.

H3C~

CH3

“o—Br

CHs

H3C~

it~CHg + BP

What this book is about and who should read it

e Propene reacts with HBr to give the bromoalkane with the structure A and not B: H

H.-C

cov ’

|

HBr CHs

HBr ~

%

H3C~

ay

5

Cc A

Br.

CH;

tr

C

H

UC.

aS

H

H

CH

3

B

Why?

You may already have come across explanations for some of these observations.

e Areason often given as to why a precipitate of AgCl is formed from Agt and Cl” ions in solution is that there is a large release of energy when

these ions form a solid lattice.

However, the precipitation of CaCO3 from a solution of Ca?+ and CO;ions is endothermic, i.e. energy is taken in. This being the case, our ex-

planation for what is going on in the case of Agt and Cl” cannot be correct! We will see in Chapter 12 why it is that both of these precipitation reactions are possible, even though one is exothermic and one endothermic. e A reason often given for why acyl chlorides are more reactive than amides is that the chlorine substituent is electron withdrawing and so makes the carbony] carbon ‘more positive’ and so more reactive towards nucleophiles such a water. The problem with this argument is that nitrogen has just about the same electronegativity as chlorine, so we would

expect it to have the same electron withdrawing effect.

Clearly some-

thing more complicated is going on here, and in Chapter explain just what this is.

10 we will

e You will find that the explanation often given for the easy formation of the (CH3)3CT ion is that the positive charge is stabilized by the electrondonating methyl groups. The question is, why, and how, do methyl groups donate electrons and why does this stabilize the cation? We will

answer this in Chapter 11.

e The result of the reaction of propene with HBr may be predicted by Markovnikov’s rule, which states that the bromine ends up on the carbon with the most alkyl groups attached to it. This just begs the question as

to why Markovnikov’s rule works — a question we will also answer in Chapter 11.

What we hope to do in this book is provide you with a logical and soundly

based set of ideas which you can use to explain why these, and many other, reactions behave in the way they do.

What this book is about and who should read it How this book is laid out

It turns out that the most fundamental principle which determines whether or not a reaction will take place is the Second Law of Thermodynamics, so we will start out by discussing this very important and fundamental concept. Powerful though this law is, it does not really help us to understand what is going on in detail in a reaction — for example, which bonds are broken, which are formed and, most importantly, why. To understand these aspects of reactions we need to look in more detail at chemical bonding.

There are two basic interactions which lead to the formation of chemi-

cal bonds: electrostatic interactions between charged species, leading to ionic

bonds, and covalent interactions in which electrons are shared between atoms. Of these, ionic bonds are perhaps the easiest to understand, so we consider

them first. In Chapter 3 we will see that we can develop a simple picture of the bonding in ionic compounds which enables us to make some useful chemical predictions. To understand how covalent bonds are formed, we need to go into quite a

lot of detail about the behaviour of electrons, first in atoms and then in progres-

sively more complex molecules. These topics are considered in Chapters 4, 5 and 6. Once we have mastered how to describe the bonding in reasonably sized

molecules — which boils down to describing where the electrons are and what

they are doing — we are ready to start considering reactions. It may seem like a long road to get to Chapter 7, but it is well worth it, as by then you will have all of the tools necessary to really understand what is going on. In the subsequent chapters we will go on to look at different kinds of reactions, introducing along the way new concepts and ideas such as the idea of reaction mechanisms and the way in which chemical equilibrium is established and influenced. The final chapters look at the crucial role the solvent plays in a chemical reaction and then at what happens when there is more than one pathway open to a reaction. How to read this book

This is not a textbook which aims to cover all the material of, say, a typical firstyear university course. Rather, this book is aimed at giving you an overview of why and how chemical reactions happen. For this reason, the text cuts across

the traditional divisions of the subject and we have freely mixed concepts from

different areas when we have felt it necessary and appropriate. Our intention is not to give a complete, detailed, description of what is going on, but rather to give an overview, bringing the key ideas into a clear perspective. If you continue your studies in chemistry you will no doubt learn about many of the ideas we introduce here in greater depth. We hope that having read this book you will have an overview of the subject so that you can see why you need to know more about particular ideas and theories and how these will help you to understand what is going on in chemical reactions.

This book will probably be most useful to those who are starting a university course in chemistry. It will also be of interest to those who are coming

to the end of pre-university courses (such as A level) and who wish to deepen

and extend their understanding beyond the confines of the syllabus. Teachers in schools and colleges may also find the text to be a useful source. We develop

What this book is about and who should read it

our argument from chapter to chapter, so the book is best read through from the beginning. Some practical matters Generally in the text we have used the systematic names for compounds, but

have also given the common names, as you are likely to encounter these much more at university level. In any case, the molecules we have chosen as examples are all rather simple and so naming them is not a great problem. When it comes to drawing molecular structures, we have included all of the carbons and hydrogens rather than simply drawing a framework as is sometimes done. Although this makes the structures a little more cluttered, it avoids ambiguity

and for simple structures does not seem to cause a problem. The only exception

-

-

we have made to this rule is that benzene rings are drawn as a framework. As you know, the four single bonds around a carbon atom are arranged so that they point towards the corners of a tetrahedron. The usual way of repre-

o

°

“,

C

Fig. 1.1 The usual representation of the tetrahedral arrangement of groups around a carbon atom.

senting this is shown in Fig. 1.1. We imagine that two of the bonds lie in the plane of the paper — these bonds a represented by simple lines. The third bond is represented by a solid wedge with its point toward the carbon; this bond is the one coming out of the page.

Finally, the fourth bond, which is going into

the page, is represented by a thick, dashed line. Where

we show pictures of atomic and molecular orbitals we have been

at particular pains to make sure that these are realistic. Often the pictures are

based on actual calculations, and so can be relied upon. Even where we have drawn sketches of orbitals we have made sure that they are realistic. So, for example, the 2p orbital is not represented as an ‘hourglass’ simply because this

is not its true shape, despite what you will see in many books! The molecules we are going to talk about are the smallest we can find

which contain the functional groups we are interested in. This makes is possi-

ble to focus on what is really important— the functional group and its electronic properties — without worrying about other details. We will also use just a few

molecules to illustrate the ideas rather than introducing numerous different ex-

amples. Again, this will allow us to focus in detail on what is going on in these

reactions.

Abbreviations

For quick reference, the abbreviations we are going to use are listed below.

Some if these may be not be familiar to you as yet, but as you read on you will come across explanations of all of these terms. 2c-2e

two-centre, two-electron

AO HAO HOMO

atomic orbital hybrid atomic orbital _highest occupied molecular orbital

LUMO

MO

lowest unoccupied molecular orbital

molecular orbital

DMF

dimethyl! formamide

DMSO _

dimethyl! sulfoxide

2

What makes a reaction go?

From experience we know that, once started, some reactions simply ‘go’ with

no further help from us. For example, gaseous ammonia reacts with gaseous hydrogen chloride to give white clouds of solid ammonium chloride:

NH3(g) + HCl(g) —> NHsCl(s). Another example is magnesium burning in oxygen — once ignited the metal burns strongly, giving off heat and light:

Mg(s) + 2O2(g) —> MgO(s). In writing these equations we used the right arrow —> to symbolize that the reaction goes entirely to the products on the right-hand side. Some reactions, rather than going entirely to products, come to equilibrium

with reactants and products both present in significant amounts. For example, the dissociation of ethanoic acid in water is far from complete and at equilibrium only about 1% of the ethanoic acid in a 0.1 M solution has dissociated: CH3COOH(aq)

+ H20(J) =

CH3COO™ (ag) +

H307* (aq).

Another example is the dimerization of NO2 to give N2Oa:

2NO2(g) = N20a(g); at 25 °C the equilibrium mixture consists of about 70% N20q4.

In these equations we use the equilibrium arrows = to indicate that the re-

action can go either way. Indeed, as you may know, at equilibrium the forward and back reactions have not stopped but are proceeding at equal rates. There is another class of reactions which simply do not ‘go’ at all, at least not on their own. For example, ammonium chloride does not spontaneously

dissociate into ammonia and hydrogen chloride, neither does magnesium oxide

spontaneously break apart to give magnesium and oxygen. Taking all of these reactions together we see that the real difference between them lies in the position of equilibrium, illustrated in Fig. 2.1. For some reactions the equilibrium lies so completely to the side of the products that to all intents and purposes the reaction is complete. For other reactions, there are significant amounts of products and reactants present at equilibrium. Finally, for some reactions the equilibrium lies entirely on the side of the reactants, so that they appear not to take place at all.

So, the question to answer is not ‘what makes a chemical reaction go?’ but ‘what determines the position of equilibrium?’. We will begin to answer this question in this chapter.

100%
N2Oa(g). On the other hand, we can approach equilibrium by starting with the pure product, N204. Experimentally, this can be achieved by increasing the pressure on the system; this favours the dimer and at high enough pressures dimerization is essentially complete. If we then decrease the pressure back to one

atmosphere some of the dimer dissociates to NO? as the equilibrium position is approached. The reaction involved is the endothermic process: N204(g) —> 2NO2(g).

We see that the equilibrium position can be approached either starting from

solely reactants or solely products. Approaching equilibrium from one side involves an exothermic process and approaching from the other side involves an endothermic process.

2.2

Entropy and the Second Law of Thermodynamics

2NOz

> N20,

_:

oe N,O, —> f 2NO3

{ L-

< ——e

exothermic

low pressure >99% NO»

endothermic

1 atmosphere 70% NoO,

high pressure >99% NzO4

Fig. 2.4 Illustration of how the equilibrium between N2O4 and NO» can be altered by altering the pressure. Since NOg is dark brown and N2QO, is colourless the shift in the position of equilibrium can easily be detected by observing the brown colour.

Clearly, it cannot be the case that the only reactions which ‘go’ are exother-

mic ones in which the products are lower in energy than the reactants. Endothermic reactions, in which the products are higher in energy than the reac-

tants, also take place and in general the approach to chemical equilibrium will involve both types of reactions. The tempting idea that reactions which ‘go’

are ones in which the products are ‘more stable’ has to be abandoned.

The reaction between ammonia and hydrogen chloride provides us with another example. If we apply sufficient heat, ammonium chloride will dissociate to ammonia and hydrogen chloride:

NH4Cl(s)

h

> NH3(g) + HCl(g).

This is another example of an endothermic reaction which can be made to “go’. The true driving force for a reaction is not moving to lower-energy products but is concerned with a quantity known as entropy and is governed by the Second Law of Thermodynamics; we will discuss both of these in the next section.

2.2

Entropy and the Second Law of Thermodynamics

The Second Law of Thermodynamics allows us to predict which processes will ‘go’ and which will not. It is therefore the key to understanding what drives

chemical reactions and what determines the position of equilibrium. The Second Law is expressed in terms of entropy changes. Entropy is a property of

matter, just like density or energy, and we need to understand what it is if we are going to apply the Second Law. The simplest description of entropy is to say that it is a quantity associated with randomness or disorder. A gas has greater entropy than a solid, as in the

gas the molecules are free to move around. A liquid has higher entropy than a solid, but lower entropy than a gas. We can rationalize this by arguing that the molecules in a liquid are more free to move than those in a solid, but not as free as those in a gas; Fig. 2.5 illustrates these points.

You may have come across the statement that ‘entropy always increases’. The idea is that any process which takes place is always associated with an increase in entropy, that is an increase in chaos or disorder. However, a moment’s

increasing entropy Fig. 2.5 The entropy of a gas is greater

than that of a liquid which in turn is greater than that of a solid. This increase in entropy can be associated with the

increasing freedom with which the molecules move as we go from a solid to a gas.

What makes a reaction go? thought reveals that there must be something wrong with this statement. After

all, if it were true, how could ice form from water? This is a process in which the entropy decreases, as ice has lower entropy than liquid water. Another

example is the reaction

NH3(g) + HCl(g) —> NH4Cl(s) in which there is clearly a reduction of ‘entropy as gaseous reactants give rise to a solid product. Yet we know that this reaction takes place.

In fact the statement ‘entropy always increases’ is almost correct, it just needs to be expressed more carefully to give the Second Law of Thermodynamics: In a spontaneous process, the entropy of the Universe increases. This statement introduces two important ideas.

Firstly, the idea of a sponta-

neous process. Secondly, that it is the entropy of the Universe that we need to consider, not just the entropy of the chemical system that we are thinking about. We will look at each of these ideas in turn.

A spontaneous process is one which takes place without continuous intervention from us. A good example of this is water freezing to ice — a process about which we will have a lot more to say in later sections. If we put water in a freezer set to —20 °C we know that ice will form; this is an example of a

spontaneous process. The reverse will never happen: at —20 °C ice will never melt to give water. Another example of a spontaneous process is the mixing of gases: once two unreactive gases are released into a container they will mix completely. The reverse, which would involve the separation of the two gases, is never observed to take place.

We can bring about the reverse of spontaneous processes by intervening.

For example, we can melt ice by applying heat and we can separate gases by using chromatography or liquefying them followed by distillation. The key point is, however, that the reverse of a spontaneous process never happens on

its own. The Second Law tells us that we have to consider the entropy change of

we think of as

the Universe, not just the entropy change of the process we are interested in.

This sounds like a tall order, but it turns out not to be as difficult as it at first

Universe

seems. We simplify things by separating the Universe into two parts: the system, which is the part we are concentrating on, such as the species involved in a chemical reaction, and the surroundings, which is everything else (Fig. 2.6).

The entropy change of the Universe can then be found by adding together the Fig. 2.6 The Universe is separated into the part we are interested in — the system, and the rest — the surroundings. For example, the system would be our chemical reactants in a beaker and the surroundings would be the bench, the laboratory and everything else in the Universe.

entropy changes of the system and the surroundings:

entropy change of Universe =

entropy change of surroundings + entropy change of system or, in symbols, t

ASuniv

=

ASsurr +

A Ssys

where ASuniy, ASsurr and ASsys are the entropy changes of the Universe, the surroundings and the system, respectively.

2.3

Entropy and heat

We shall see in the next section that in an exothermic process the heat given out increases the entropy of the surroundings. This increase can compensate for a decrease in the entropy of the system so that overall the entropy of the Universe increases. This is why water can freeze to ice and NH3 can react with HCI. These processes involve a reduction in entropy of the system but they are sufficiently exothermic that the surroundings increase in entropy by enough to make the entropy of the Universe increase. These are rather subtle points, which

we will tease out in the next few

sections. The first thing to discuss is how the exchange of heat can lead to an

entropy change and how the temperature affects the size of this entropy change.

2.3

Entropy and heat

Imagine an exothermic reaction which gives out heat to a nearby object. What effect does this have on the entropy of the object? We know that absorbing heat increases the energy of the molecules in the object and so causes them to move around more. We have seen before that more motion — increasing disorder — is associated with an increase in entropy. It is therefore not surprising to find that when an object absorbs heat its entropy increases (Fig. 2.7). A further consequence of the heat being absorbed is that the temperature of the object increases, so we can also see that raising the temperature of an object increases its entropy. Conversely, if heat flows out of an object, its entropy decreases. What happens, then, if the object we are supplying heat to is very large —

for example the surroundings, which comprise all of the Universe apart from the system? The temperature of such a large object as the rest of the Universe

is not going to be affected by the amounts of heat which typical chemical processes produce — put another way, we are not going to heat up the rest of the

Universe significantly by leaving the oven door open! Nevertheless, although the temperature of the surroundings has not changed, they have absorbed en-

ergy (in the form of heat) and, as described above, this leads to an increase in

the entropy. In summary:

In an exothermic process the system gives out heat to the surroundings and so the entropy of the surroundings is increased. In an endothermic process the system takes in heat from the surroundings and so the entropy of the surroundings is decreased.

We can apply these ideas right away to understand how it is that water can freeze to ice. To melt ice to water we need to apply heat, so ice

— water is an

endothermic process. This makes sense, as in melting ice we are beginning to break the hydrogen bonds between the molecules. The reverse process, water — ice, in which bonds are being made, is therefore exothermic.

Ice has lower entropy than liquid water, so on freezing the entropy of the

system decreases.

However, the process is exothermic, so the entropy of the

surroundings increases. It must be that the increase in entropy of the surroundings is sufficient to compensate for the decrease in entropy of the system so that

Fig. 2.7 When an object absorbs heat the molecules move more rapidly and so its entropy increases.

What makes a reaction go?

10

IEE 4 ons ie

=

entropy of system decreases | >

y

entropy of the surroundings increases Fig. 2.8 When ihe heat given spontaneous, the system so

water freezes out results in the increase in that overall the

entropy of the

Universe increases

4

to ice its entropy decreases; however, the process is exothermic and an increase in the entropy of the surroundings. For this process to be entropy of the surroundings must outweigh the decrease in entropy of entropy of the Universe increases.

overall the entropy of the Universe increases. The overall process is illustrated in Fig. 2.8. Coming back to the reaction we discussed above NH3(g) + HCl(g) —> NH4Cl(s) NH.(9) 39.

HCI(g)

entropy of system decreases

NH,Cl(s)

heat entropy of surroundings increases

Fig. 2.9 When gaseous HCl reacts with gaseous NHg, solid NH4Cl is formed; there is consequently a reduction in entropy of the system.

However, the

reaction is exothermic and the heat given out increases the entropy of the surroundings.

Overall, the entropy

increase of the surroundings outweighs the decrease in entropy of the system, so the entropy of the Universe increases

and the process is spontaneous.

we see that there is a decrease in the entropy of the system as a solid is formed from gases. In solid NH4Cl there are strong interactions between NHj and CI” ions and so it is not surprising to find that the reaction is exothermic; it follows that the entropy of the surroundings increases. These entropy changes are illustrated in Fig. 2.9. As the reaction is spontaneous it follows from the Second Law that the increase in entropy of the surroundings must outweigh the decrease in entropy of the system, giving an overall increase in the entropy of the Universe.

There is one more subtlety to sort out here. Water freezes to ice only if the temperature is below 0 °C; at higher temperatures the water remains liquid. Water solidifying to ice is always exothermic, and as a result the entropy of the surroundings would always increase.

However, it seems that this increase

in entropy is only sufficient to compensate for the decrease in entropy of the

system when the temperature is sufficiently low. We will see in the next sec-

tion just exactly how and why temperature affects the entropy change of the surroundings.

2.4

Role of temperature

The entropy increase resulting from supplying a certain amount of heat to an

object depends on its temperature. We can understand this in the following way. Suppose that the object is very cold so that the molecules are not moving around very much. Supplying some heat will make the molecules move around more,

and so the entropy increases.

Now

suppose that we apply the same

amount of heat to a much hotter object in which the molecules are already moving around a great deal. The heat will cause the molecules to move even

more vigorously, but the change is much less significant in the hotter object than in the cooler one, simply because in the hotter object the molecules are

already moving more vigorously in the first place. We conclude that supplying heat to a hotter object causes a smaller increase in entropy than supplying the same amount of heat to a cooler object; this is illustrated in Fig. 2.10.

2.4

Role of temperature

11 ~

increase in entropy

, os On

‘’

warmer

smailer increase in entropy

—

{vo

—

io

a little hotter

Fig. 2.10 Supplying heat to a cool object, in which the molecules are not moving very much, causes a larger increase in entropy than does supplying the same amount of heat to a hot object in which the molecules are already moving vigorously.

For the surroundings, which are very large, the entropy change can be computed very simply from: entropy change of the surroundings =

heat absorbed by the surroundings .

temperature of the surroundings

Using symbols we can write this as (2.1) where qsurr and Tsurr are the heat absorbed by and absolute temperature of the surroundings, respectively. Heat is normally measured in joules and temperature in kelvin, so it follows from Eq. 2.1 that the units of the entropy change (and of entropy) are J K~!. In chemistry we often quote molar quantities, that is the entropy change per mole,

in which case the units are J K~! mol7!.

Equation 2.1! can only be used to compute the entropy change of the surroundings. Finding the entropy change of the system requires a different approach which we will not discuss here but simply note that the absolute entropies (as they are called) of many substances have been determined and tables of these can be found in any standard text. Such tables also list the entropy change associated with phase changes, such as ice melting to water. With the aid of such data we shall, in the next section, use the Second Law to explain

why it is that the temperature has to be below 0 °C for water to freeze. How

The and the and

to make ice

approach we will adopt is to compute the entropy change of the system of the surroundings; adding these together gives us the entropy change of Universe, ASyniy. If this is positive, the entropy of the Universe increases from the Second Law we know that the process can take place. If A Suniv

is negative, that is the entropy decreases, we know that the process cannot take

place, as it is forbidden by the Second Law. From tables we can find that the entropy change for ice — water is 22.0 J K~! mo!7!. As expected, this is a positive number since disorder is

Some typical values of absolute entropies at 298 K:

He(g): 126 J K~! mol7! Ho(g): 131 J K~* mol7!

Hg(/): 76 J K71 mol7* Cu(s): 33 J K71 mol-1

What makes a reaction go?

12

increasing.

We are interested in the change water —

ice, for which the en-

> water. The entropy change of the

tropy change is simply minus that for ice

system, AScys, is therefore —22.0 J K~! mol™!.

To compute the entropy change of the surroundings using Eq. 2.1 we need to know the amount of heat absorbed by the surroundings. This heat can only come from the system. If the system gives out heat in an exothermic process

surroundings

a

surroundings

In summary, from the point of view of the surroundings, the heat is travelling in the opposite direction to that of the system; Fig. 2.11 illustrates these points.

We can therefore write:

exothermic

endothermic

sys Negative Asurr POSitive

sys Positive Qsurr Negative

Fig. 2.11 Illustration of the heat flow between the system (the black circle) and

the surroundings. results in the flow surroundings; an results in the flow surroundings.

(i.e. qsys is negative), the surroundings must be absorbing this heat, making sur positive. On the other hand, if the process in the system is endothermic (i.e. Gsys iS positive) the heat that the system absorbs must come from the surroundings. The surroundings are therefore losing heat, making gsurr negative.

An exothermic process of heat into the endothermic process of heat out of the

Gsurr = —4sys

where qsurr is the heat absorbed by the surroundings and qgys is the heat absorbed by the system. From tables we can easily find that the heat needed to melt ice to wa-

ter (called the heat of fusion) is 6010 J mol7!; as expected, this is positive. We are interested in the process water — ice, which is the reverse of melting, so the heat for this is simply minus that for melting ice to water: Gsys = —6010J mol—!. Therefore, when water freezes to ice, this heat is given to the surroundings so qsurr = 6010 J mol~!, We can now compute the entropy change of the surroundings. First, we

will do this at 5 °C, which is 278 K: A Ssurr

=

Gsurr Tsurr

_ 6010 ~ 278 21.6) K7! mol7!. We already know that ASsys = —22.0J K~! mol7! so we can find the entropy

change of the Universe as follows: ASuniv

=

ASsur

+

ASsys

= 21.6 — 22.0

= -0.4JK7! mol!. The entropy change of the Universe is negative, meaning that the entropy has decreased. Such a process is forbidden by the Second Law and so we conclude

that water cannot freeze at 5 °C. Now, let us repeat the calculation at —5 °C, which is 268 K: A Ssurr

=

surr SUIT

_ 6010 ~~ 268 22.43 K7! mol7!,

2.5

Exothermic and endothermic reactions ASuniv

=

ASsur

13

+ ASsys

= 22.4 — 22.0

= 0.43 K7! mol7!. At this lower temperature the entropy change of the Universe is positive, meaning that the entropy has increased. So, the process is allowed by the Second Law and at this lower temperature water can freeze to ice.

It is important to notice that what has changed between 5 °C and —5 °C is

the entropy change of the surroundings.

Furthermore, the reason that A Ssur

has changed in size is simply due to the temperature change; the heat given to the surroundings has remained the same. Due to the way in which we compute ASsurr (Eq. 2.1), for a given amount of heat the size of the entropy change can be altered simply by changing the temperature of the surroundings. It is now clear why we put water in a freezer in order to make ice (Fig. 2.12). The process of water going to ice is associated with a reduction in the entropy of the system. For this to be allowed by the Second Law, the reduction in entropy must be compensated for by an increase in the entropy of the surround-

water IES on,

entropy decreases

ice

ings. Such an increase comes about when the surroundings absorb heat, as will

be the case for an exothermic process such as water freezing. However, the entropy change of the surroundings depends on their temperature. The lower the temperature, the greater the entropy change. So, water will only freeze once the temperature of the surroundings is low enough that the increase in their entropy is large enough to compensate for the decrease in entropy of the water

as it freezes.

So, the reason why we put water in the freezer when we want to make ice is so that the entropy change of the surroundings (inside the freezer) is large enough to compensate for the entropy decrease of water freezing. It can be

hard to explain this to people who think that the freezer “sucks the heat out of the water’!

Why all this fuss about making ice?

You may well be asking yourself why it is that we are discussing making ice in a book devoted to understanding chemical reactions! The reason for this is that it is easier to describe how the Second Law applies to a physical process such

as water freezing to ice than it is to apply it to chemical equilibrium. However,

we can use the tools we have developed so far to understand some reactions which either go entirely to products or do not go at all; these are the subject of the next section. Later, in Chapter 8, we will return to the discussion of

chemical equilibrium. 2.5

Exothermic and endothermic reactions

Using the Second Law and the idea of separating the entropy change of the Universe into the entropy change of the system and the surroundings, we can begin to understand why some chemical reactions go. We have already dis-

cussed the reaction

NH3(g) + HCl(g) —> NH4Cl(s)

surroundings entropy increases Fig. 2.12 When water solidifies to give ice, the entropy of the system decreases. However, the process is exothermic and

so the entropy of the surroundings will be raised as they absorb the heat. The process will only be spontaneous if the surroundings are cold enough that their entropy increase outweighs the entropy

decrease of the system, thus making the entropy of the Universe increase.

What makes a reaction go?

14

in which there is a reduction in entropy of the system. However, as the reaction

is exothermic the entropy of the surroundings increases, and this compensates

for the decrease in entropy of the system. Another example is the precipitation of solid AgCl from solution (illustrated in Fig. 2.13):

Ag* (aq) + Cl” (aq), — AgC\(s). entropy of system decreases

entropy of the heat +> Surroundings increases

AgCl(s) Fig. 2.13 The precipitation of solid AgCl

by mixing solutions containing Ag*t and

CI” ions is a spontaneous process. The entropy of the system decreases as a solid is formed from two solutions; however, the process is exothermic, resulting in an increase in the entropy of the surroundings which must outweigh

the decrease in entropy of the system so that overall the entropy of the Universe increases.

Again, there formed. In solid ions; however in water molecules. on the particular

is a reduction in entropy of the system, as a solid is being AgCl there are strong interactions between the Agt and Cl solution these ions have favourable interactions with the polar Which of these two sets of interactions are stronger depends ions in question but it turns out for AgCl that the interactions

in the solid are the stronger, so the above reaction is exothermic. As a result there is an increase in the entropy of the surroundings. Since we know that

the precipitation takes place it must be allowed by the Second Law increase in entropy of the surroundings must outweigh the decrease of the system. We can simply turn this discussion round and use it why solid AgCl! does not dissolve in water as such a process would

and so the in entropy to explain involve a

decrease in the entropy of the Universe and so cannot occur. Reactions which involve an increase in the entropy of the system do not necessarily need to be exothermic to be allowed by the Second Law. For example, dissolving solid ammonium nitrate in water, illustrated in Fig. 2.14, involves an increase in the entropy of the system because the ions which were held in the crystal lattice are free to move in solution — there is an increase in

disorder. For ammonium nitrate it turns out that the interactions between the ions in the solid are stronger than those between the ions and solvent water, so

forming the solution is an endothermic process. This means that the entropy of the surroundings decreases. We know that ammonium nitrate dissolves, so it must be that the entropy increase of the system overcomes the entropy decrease

of the surroundings so that the Second Law is obeyed. entropy of system increases i = heat taken in H,0()

NH,NO,(s)

from surroundings entropy of the surroundings decreases

entropy of the Universe increases NH,NO,(aq) 4

Fig. 2.14 When ammonium nitrate dissolves in water there is an increase in the entropy of the system as the solution is more ‘random’ than the solid plus liquid which we start with. Dissolving this salt turns out to be endothermic, which means that heat is absorbed from the surroundings resulting ina decrease in their entropy. The process is spontaneous at room temperature, so we conclude that the entropy increase of the system must outweigh the entropy decrease of the surroundings so that the entropy of the Universe increases.

A contrast to ammonium nitrate dissolving in water is when solid sodium hydroxide dissolves. As before, the entropy change of the system is positive but

this time the process is exothermic so the surroundings also increase in entropy. The entropy of the Universe increases unconditionally and so the Second Law is obeyed.

2.6

How do we know all this is true?

15

As was discussed in Section 2.4 on p. 10, temperature plays an important role in determining the size of the entropy change of the surroundings. A good example of the effect of this is in dissociation reactions such as

N204(g) —> 2NO2(g).

Since two moles of gas are produced from one there is an increase in dis-

order and the entropy of the system increases. This reaction is endothermic, resulting in a decrease in the entropy of the surroundings. The key thing is that the size of this decrease depends on the temperature of the surroundings, as can be seen directly from the way in which the entropy change of the surroundings is calculated: AScurr = surr/Tsurr- Increasing the temperature decreases the size Of ASsurr simply because of the division by Tsu; Fig. 2.15 illustrates this point.

For the dissociation reaction, when the temperature is low the entropy decrease of the surroundings outweighs the entropy increase of the system and so the reaction does not take place as it would result in a decrease in the entropy of the Universe, in violation of the Second Law. At higher temperatures, the entropy change of the surroundings is smaller in size and eventually it ceases to outweigh the entropy increase of the system. Then the dissociation can take

place as it is allowed by the Second Law.

Another example of a dissociation reaction is solid MgO going to gaseous

atoms:

MgO(s) —> Mg(g) + O(g).

This is a rather strange looking reaction, but at high enough temperatures it will take place. The argument goes as follows: firstly, we note that the entropy of the system increases as gases are formed from a solid. Secondly, the reaction is endothermic as in forming the gaseous atoms strong interactions in the crystal lattice are broken up. So, the reaction is analogous to the dissociation of N2O4 and will only take place when the temperature is high enough. In the case of MgO this turns out to be a very high temperature as the reaction is much more endothermic than is the dissociation of N2Qx4. In summary, to be allowed by the Second Law a process which leads to a decrease in the entropy of the system must be exothermic. A process which leads to an increase in the entropy of the system can be either exothermic or endothermic. The temperature of the surroundings is also important as this affects the magnitude of the entropy change of the surroundings.

2.6

How do we know all this is true?

In this chapter we have simply asserted the truth of the Second Law of Thermodynamics and have also introduced a definition of entropy without much justification. How do we know that these ideas and definitions are correct, and

where do they come from? To answer these questions is by no means a simple task — it would involve a detailed study of thermodynamics, and we simply do

not have room to go into this now.

these assertions.

So, for now we ask you simply to accept

increasing temperature Fig. 2.15 Illustration of the way in which the entropy change of the Universe is affected by an increase in temperature. On the left, the entropy change of the system is positive (upward pointing arrow), but the entropy change of the surroundings is sufficiently negative that it outweighs the entropy increase of the system and so the entropy of the Universe decreases.

Increasing the

temperature reduces the magnitude of the entropy change of the surroundings and, as shown on the right, eventually the entropy change of the Universe

becomes positive.

16

What makes a reaction go? Like all physical laws, the truth of the Second rests On experimental observations and these show very strong law indeed. In fact no process which ond Law has ever been observed. We can happily understanding chemical reactions in the knowledge

Law of Thermodynamics that the Second Law is a is in violation of the Secapply the Second Law to that it will not let us down.

hy

2.7

The Second Law and Gibbs energy

It is not really convenient to have to think about the entropy change of the system and the surroundings in order to apply the Second Law. A more convenient approach is to define a quantity called the Gibbs energy which can be computed from properties of the system alone. We will show how the change in Gibbs energy is related simply to the change in the entropy of the Universe so that it is possible to apply the Second Law once the change in Gibbs energy is known.

We saw before that we can separate the entropy of the Universe into a part

referring to the surroundings and a part referring to the system: ASuniv

=

A Ssurr +

ASsys.

(2.2)

We also saw that the entropy change of the surroundings can be computed from

the amount of heat absorbed by the surroundings ASsurr

=

dure >

(2.3)

SuIT

and that this heat absorbed is opposite to that absorbed by the system Ysurr = —sys:-

(2.4)

If we used qsurr from Eq. 2.4 in Eq. 2.3 and then put the resulting expression for ASsurr into Eq. 2.2 we have a new expression for A Syniy A Suniv

=

—4sys

sys

+ ASsys

(2.5)

in which we have assumed that the system and surroundings are at the same temperature, so Tsyy = Tsun (we will do this from now on). The nice thing about Eq. 2.5 is that all of the quantities on the right-hand side refer to the

system — we do not have to worry explicitly about the surroundings.

Under conditions of constant pressure, sys 18 identical to the enthalpy change of the system, given the symbol AH. Chemists virtually always work

under conditions of constant pressure, so the identification of Qsys with the enthalpy change is certainly appropriate. Using this, Eq. 2.5 becomes A Suniv

=

—AFsys sys

+

ASsys.

We now introduce the Gibbs energy, given the symbol

(2.6)

G.

For a process the

change in the Gibbs energy of the system, AGsys, is defined as AGgys

=

A Hgys

_~ TsysA Ssys

(2.7)

2.7

The Second Law and Gibbs energy

17

where Tsys is the absolute temperature, in kelvin.

For reasons which will be-

come clear in a moment, we divide both sides of Eq. 2.7 by —Tsys to give —AGsys

_

—AHgys

Tsys

Tsys

+ ASsys-

(2.8)

Comparing Eq. 2.8 with Eq. 2.6 we have A Suniv

=

—AG

—_—*

sys

In words, —AGsys/Tsys is exactly the same thing as the change in entropy of the Universe. A process which is allowed by the Second Law has a positive value for ASuniv and therefore has a positive value for —AGsys/Tsys; hence AGsys must be negative. A positive value for AGgys implies a negative value for ASuniy, and so such a process would not be allowed by the Second Law. We see that once AGgys is known, we can simply inspect its sign to determine whether or not the process is allowed by the Second Law. The convenient thing about this approach is that AGsy; is computed only from properties of the system — we do not need to worry directly about the surroundings. Indeed, from

now on we will drop the ‘sys’ subscript and simply assume that we are dealing with the properties of the system.

Making ice — again! To illustrate the use of the Gibbs energy we will go through the same calcu-

lation as in Section 2.4 on p. 10 about making ice. All we need to do is to

compute AG for the process water — ice using AG = AH

—TAS.

We already know that the heat absorbed by the system in going from water to ice is —6010 J mol™!; in fact this value is for the change at constant pressure and so is equal to AH. We also know that the entropy change is —22.0J K~! mol7! and so it is easy to compute AG. At 5 °C (278 K) this is

AG = AH —TAS = —6010 — 278 x (—22.0) — 106 J mol7!. Note that the units of the Gibbs energy are joules, or for molar quantities, joules per mole. We see that at 278 K, AG is positive; this implies that the process cannot take place as it is in violation of the Second Law. At —5 °C (268 K) the calculation is

AG = —6010 — 268 x (—22.0) = —114J mol™!. Now AG is negative and so the process can take place as it is in accord with the Second Law. The conclusions are as before, but the calculations are somewhat easier as we only have to think about the system, not the surroundings.

Remember that Tsys is in kelvin and so

is always positive.

Processes which are allowed by the Second Law of Thermodynamics have ASuniy > 0 which is the same thing as having AGsys

< 0.

What makes a reaction go?

18

2.8

Gibbs energy in reactions and the position of equilibrium

In Section 2.1 on p. 6 we spent some time pointing out that energy changes are not the criterion for deciding whether or not a reaction will ‘go’. We have now

seen that the criterion for whether or not a process can take place is the sign of ASuniy which is reflected in the sigmof ‘AG. If it is negative, the process is

allowed by the Second Law and so can take place; if it is positive, the process is not allowed by the Second Law and so cannot take place. For a chemical reaction AG means ‘Gibbs energy of the products — Gibbs energy of the reactants’, just in the same way that AZ is defined. So, if AG is negative, it means that the products have lower Gibbs energy than the reactants. The driving force for a chemical reaction can therefore be described as going to products which have lower Gibbs energy than the reactants. Note that it is the Gibbs energy which has to be lowered, not the energy. There are two contributions to the Gibbs energy: an enthalpy term, AH, and an entropy term, AS: AG

A negative value of AH

= AH

-TAS.

(i.e. an exothermic reaction) and a positive value of

AS both contribute to making AG negative, and hence a reaction which ‘goes’. If AZ is large and negative, the sign of the entropy term is unimportant as the

—T AS term is swamped by the AH term. This is why it seems that having a large negative AA (i.e. a strongly exothermic reaction) results in a reaction which goes to products.

It is for this reason that in much of the discussion that follows we will

be concentrating on energy (enthalpy) changes and trying to identify reaction pathways which lead to the greatest reduction in energy. The chances are that such reactions will be favoured because of their negative AH values. The entropy term plays a much more important role when it comes to reactions

involving ions in solution, a topic which we will consider in Chapter 12.

The position of equilibrium At the beginning of this chapter we pointed out that the important thing to understand about a reaction is the position of equilibrium. So far we have introduced the idea that by inspecting the sign of AG we can determine whether

or not a process is allowed by the Second Law.

We have not, however, ex-

tended this to the more subtle point of determining the position of equilibrium.

We will do this in Chapter 8, but for the moment we will simply concentrate on looking at reactions from the point of view of energy changes.

2.9

Where does the energy come from?

The energy change which accompanies a reaction is due to the making and breaking of chemical bonds: energy is given out when a bond is formed, and taken in when one is broken. As energy changes are very important in deter-

mining whether or not a reaction will go, we need to understand the factors which influence the energies involved in making and breaking bonds.

2.9

Where does the energy come from?

There are two extremes of bonding: one is when electrons are shared equally between two atoms in a covalent bond, the other is when two charged groups are held together by electrostatic interactions (i.e. the attraction between opposite charges). The vast majority of bonds fall somewhere between these

two extremes, with the electrons in the bond being shared unequally between the two atoms, thus giving a polar bond.

Later on we will discuss the nature of covalent bonding, but first we will

look at the bonding due to purely electrostatic interactions. As we shall see, such bonds are particularly strong and so their formation is a powerful driving force for a reaction.

19

3.

lonic interactions

In the previous chapter we saw how energy changes are crucial in determining whether or not a reaction will take place.

There are two major sources of

energy in chemical reactions: interactions between charged species (ions) and

the making and breaking of covalent bonds. Ionic interactions are probably the easiest to understand so we will discuss these first before moving on to the

more complex topic of covalent bonding. This chapter will only consider the interactions between ions in solid materials; ions in solution are of course very important in chemistry but are more complex to describe and so we will delay

this until Chapter 12.

3.1.

lonic solids

That solid sodium chloride is made up of positively charged sodium ions and

negatively charged chloride ions is such a familiar idea that we are perhaps in danger of taking it for granted, so we will spend a few moments reviewing the

#

a

Sy

@na

evidence for the existence of ions in such solid materials. The best evidence comes from X-ray diffraction studies which can both

\

eae’,

f

1

Ocr

Fig. 3.1 Representation

of part of the

lattice of solid NaCl as determined by X-ray diffraction.

locate the positions of the nuclei and also map the electron density between them. Such studies show that the sodium and the chlorine atoms are arranged

in a regular lattice, as depicted in Fig. 3.1, and that the charge on the chlorine

and sodium atoms is close to one unit. Furthermore, it is found that between adjacent sodium and chlorine nuclei the electron density falls to a very low

value. These observations are consistent with the almost complete transfer of an electron from sodium to chlorine, leading to the formation of ions with little electron density between them. X-ray diffraction studies also allow us to measure the distances, r(MX),

between the ions in the lattice.

If we look at this data for the series of salts

MBr and MC], where M is any of the Group I metals (Li, Na, K, Rb, Cs), we find that the difference r(MBr) — r(MCl) varies by only a few percent as we change M. Similarly, if we look at the difference r(RbX) — r(KX), where X is one of the halogens, there is little variation from halogen to halogen. These observations lead to the idea that each ion can be assigned an ionic

radius which is more or less independent of the salt in which the ion is present. So, for example, the Na—Cl distance can be found by adding together the ionic radii of Na* and Cl-; the same value of the ionic radius of Cl~ can be used to find the K—-Cl distance in solid KCI. That tables of such ionic radii can be drawn up suggest that, to a large extent, the ions can be thought of as behaving independently in the solid. There are some physical properties which are often taken as being indicative of the presence of ions in a solid. For example, such solids are generally insulators but, on melting, the electrical conductivity rises sharply; this is at-

3.2

Electrostatic interactions

21

tributed to the ions being immobile in the solid but free to move in the liquid.

The energy of interaction between charged species, such as ions, has a simple form and we will be able to exploit this in the next section to develop a straightforward expression for the total energy of the ions in a lattice. We will

then go on to see how this expression can be used to understand the energetics of the formation of a lattice and rationalize the outcome of some reactions involving solids.

3.2

Electrostatic interactions

In this section we are going to calculate the energy of interaction between the ions in a lattice just by considering the ions as charged objects. As you know, oppositely charged objects attract one another — that is there is a force between

them, we call this the electrostatic or Coulomb interaction. This force is found

to be proportional to the charges involved and inversely proportional to the square of the distance, r, between the two charges. The force is given by force =

where

qi

and

a fundamental

q2

are

the two

4142

4n €or

charges

5

(in units

constant called the vacuum

8.854 x 1071? Fm7)),

of coulombs),

permittivity

and

¢9 is

(it has the value

The energy of interaction of two charges, which is what we are interested in, is given by 4142

energy =

Ameor’

(3.1)

which is properly described as the electrostatic (or Coulomb) potential energy.

Note that it varies inversely with the distance in contrast to the force which varies as the inverse square of the distance.

The charge on an ion can be thought of as the result of an atom gaining or losing a whole number of electrons, which means that the charge can be expressed as a multiple of the charge on the electron, e (which is

1.602 x 10~!9C). So fora singly charged negative ion the charge is —e, for a

doubly charged negative ion the charge is —2e and so on. Similarly, singly and

doubly charged positive ions have charges of +e and +2e, respectively. We need to be careful to distinguish the numerical charge on the ion, which

is an integer, and the actual charge on the ion, which is some multiple of e. The numerical charge of a positive ion will be written as z+ and that of a negative ion as z.; z and z_ are always positive numbers, even for negatively charged

ions. The charge on a positive ion is z;e and on a negative ion is —z_e; note the introduction of the minus sign for the negatively charged species.

Putting these values for the charges qi and q2 into Eq. 3.1, the energy of interaction of a positive and negative ion with numerical charges z4 and z_,

respectively, is

energy = —

z4z-e* 4reor

(3.2)

The expression is negative, indicating that there is a lowering of the energy due to this favourable interaction between opposite charges.

Ionic interactions

22

Figure 3.2 shows a plot of this energy as a function of the distance between

the charges; the closer the two charges come, the more negative the energy. At

ze e

a

®Cc

Mm

-ze@ e

o

0

large values of r the energy goes to zero, but on account of the 1/r dependence, this approach to zero is rather slow. The graph shows us that two oppositely charged ions will move towards each other, if they are able to, since this will lead to a lowering in the energy. We will now use this expression to discuss the energetics of the formation of an ion pair. Forming an ion pair

Fig. 3.2 Plot showing how the energy of

interaction of two opposite charges varies with the distance between them.

The energy is negative as the interaction is favourable, and the closer the ions are to one another the more negative the

Imagine we have sodium and chlorine atoms in the gas phase. Given what we know about these two elements, we might reasonably expect the sodium to lose an electron to form Nat and the chlorine to pick this electron up to form Cl”. The two oppositely charged ions would then be attracted to one another, and so might form an NaCl molecule which we imagine to be an ion pair, NatCl-. The whole process can be written:

Na(g) +CKg) ts

energy becomes.

Nat(g) +Cl-(g) —+> NatCl“(g).

E) is the ionization energy of sodium, and has the value 502 kJ mol—!; E> is

the electron affinity of chlorine, which is the energy of the process

Cl(g) The The are and

+e7 —> CI (g).

value of the electron affinity is —355 kJ mol7!, so E; +E? is 147 kJ mol~!, fact that E, + E2 is positive tells us that when a sodium and chlorine atom far apart it is not favourable simply to remove an electron from the sodium add it to the chlorine.

However, when the two oppositely charged ions come together there is a favourable energy of interaction, as shown by Fig. 3.2 — this means that E3

will be negative. The closer the ions come together the more negative F3 will become, eventually cancelling out the 147 kJ mol~! (which is E} + E2) and so making the overall process exothermic.

The usual expectation for molecules is that there tance, the equilibrium distance, at which the energy imum. However, this will not be the case for these Coulomb interaction; all that happens to them is that on decreasing as the ions approach — there will be no which is simply not a realistic situation.

will be a particular disof interaction is a mintwo ions experiencing a the energy goes on and minimum in the energy,

What is missing from our model is that at short enough separations even

ions of opposite charge will begin to repel one another due to interactions between their electrons. This repulsive interaction is much shorter range than the Coulomb interaction and typically varies inversely as some high power of r: ]

repulsion energy « —

rn?

where So makes action

n is between 5 and 12; it is around 8 for Na and Cl. what we have is a balance between the electrostatic interaction which the energy more negative as the ions get closer, and this repulsive interwhich makes the energy increase. The result is that there will be some

3.2

Electrostatic interactions

23

750 repulsive term

| 500+ g

250 y

mR

0

2 5

7 :

|

5 -250b 500 750 Lb

totalenergy 4

energy

of the

| ------ energy

of the

tee separated ions

10

12

r/K ——~+

14

separated atoms

of f

/ NaCl(s). E4 is greater in magnitude than E3 by a factor of M (1.75) which is rather significant. So, forming the lattice is a much more exothermic process than

forming the ion pairs. The case of forming MgO shows up this difference even more dramatically: 2

E

+ O?-(g) —2> + O(g) —1t#2s Mg2+(g) Mg(g)

_

Mg?+0?-(g).

Now E] + E> is 2807 kJ mol~! and using an internuclear separation of 2.1 A we find E3 is —2266 kJ mol~!.

Thus, the process of forming the ion pairs is

endothermic and so unlikely to be favourable. However, if we form a lattice rather than the ion pairs

O(g) its Ma(g+ )

+ O7-(g) —*> MgO\(s), Mg?*(g)

we find that E4 is now —3961 kJ mol~!, making the overall process exothermic. So, forming ion pairs is endothermic, but forming the lattice is exothermic

Ionic interactions

26

~anice illustration of the large extra lowering in energy to be had from forming

the lattice.

We should end on a note of caution here. Species such as NaC] and MgO are known in the gas phase, but their internuclear separations are significantly less than the corresponding separations in the crystal. This is taken to imply

that the bonding in these simple diatomics is not entirely ionic but has a signif‘ icant covalent component. ‘Ny

3.3

Estimating lattice energies

The Born—Landé equation, Eq. 3.4, is an expression for the energy of interaction between the ions in a crystal lattice. Usually, when we are thinking about the energetics of solid lattices we talk in terms of the lattice energy which is the energy needed to take the ions from the lattice into the gas phase where they

are so far apart that they are not interacting. For NaCl the process is

NaCl(s) —> Na*(g) + Cl” (g). The energy of the ions in the lattice is given by Eq. 3.4 and as the gaseous ions

are not interacting at all their electrostatic energy is zero.

Hence the lattice

energy is just minus the energy given by Eq. 3.4:

MN 1 lattice energy = MAZHE€ A ITEQrO _e* ( _ -) . n

(3.5)

Strictly speaking this expression gives the change in what is called the internal energy, rather than the enthalpy; what is more the energy is for a process taking place at 0 K. It is possible to correct the value to give the usual enthalpy change at 298 K, but the correction is small and not really of any significance for

the calculations we are going to do here. We will simply use Eq. 3.5 as an expression for the lattice enthalpy, which is the enthalpy change of going from the solid to the gaseous ions.

Let us use Eq. 3.5 to estimate the lattice energy of NaCl.

For this crystal

the value of ro determined by X-ray diffraction is 2.81 A, the appropriate value

of n is 8 and, as already mentioned, the Madelung constant is 1.748.

These

data are all we need ta compute the lattice energy as 754 kJ mol~!, a value

which compares very favourably with the accepted value of 773 kJ mol~!. It is remarkable that this very simple model produces such a good estimate of the lattice energy.

A similar calculation for MgO (ro = 2.00 A) gives the lattice energy as 4043 kJ mol~!. This value is much larger than that for NaCl on account of the

much stronger interactions between the doubly charged Mg?*+ and O27 ions in MgO.

It is striking how large these lattice energies are, indicating that the

interaction between ions is a very significant contributor to the energy changes in chemical processes.

3.3

Estimating lattice energies

27

Ionic radii

We mentioned right at the start of this chapter (p. 20) that in a crystal it is pos-

sible to assign a radius to each ion, the value of which is broadly independent

of the lattice in which the ion is found. This is very useful to us as it means that

we can compute the equilibrium separation, ro, needed in Eq. 3.5 as the sum of

the radii of the positive and negative ions, ry and r_, respectively: ro=rat+r_.

So, if we want to work out the lattice energy of a compound, rather than need-

ing to know the value of ro (which would require X-ray diffraction experiments

on the crystal) we can simply look up the ionic radii from tables. Some typical values of ionic radii (in units of A) are shown in the table below:

cations

z=

Lit Nat Kt Rb*+

1

0.68 1.00 133 1.47.

anions

z=

Mg*t Ca*+ Sr Batt

2

0.68 0.99 1.16 1.34

z_=1

FCIBr~ I-

1.33 1.82 1.98 2.20

z=

O*% S*Se*Te*-

1.42 1.84 1.97 2.17

There are some general trends evident from this table: e as we go down a group the radii increase; e for elements in the same row of the Periodic Table, 2+ ions are smaller than 1+ ions;

e anions are generally larger than cations; e for elements in the same row of the Periodic Table, 2— ions are larger

than 1— ions.

It makes sense that 2+ ions are smaller than 1+ ions, as when an electron is

removed the remaining electrons are held more tightly and so are pulled in by their attraction to the nucleus. Similarly, the increased size of anions is due

to the electrons experiencing less attraction to the nucleus.

In the following

chapter we will look in more detail at the interactions which are responsible

for these changes. We should be aware of the limitations of such tables of ionic radii. Usually they have been ‘adjusted’ to give, on average, the best estimates of the lattice energy. Different people have different ideas of the best adjustments to make, so you will find that the values of ionic radii quoted in one book are often different to those quoted in another! For a particular lattice the value of ro determined by using these tabulated ionic radii is best regarded as a reasonable estimate, and so the value of the lattice energy we determine must be treated with caution. It will not be more precise than a few percent, at best.

Ionic interactions

28

The Kapustinskii equations The Russian scientist A. F. Kapustinskii noticed that the ratio

M/v, where M

is the Madelung constant and v is the number of ions in the molecular formula, varied rather little from crystal structure to crystal structure. He proposed that a good compromise was to take the value for this ratio as 0.874, thus enabling the value of M to be written as 0.874v. Kapustinskii also proposed that a typical

value of n = 9 should be used in. Eqa3.5. With these two simplifications the

expression for the lattice energy becomes:

lattice energy =

0.874vNaz4z-e7 (: Anmeo(r4, +r—)

;) a)9

where we have replaced ro by (r+ + r_). Putting in the values of all the con-

stants we find the following rather simple expression for the lattice energy

lattice energy/ kJ mol~! =

1070 v z4z(rz +r)

3.6

(3.6)

where the ionic radii are in A.

For NaC! there are two ions in the molecular formula, so v = 2; from tables

we find the radius for Nat to be 1.00 A and for CI

to be 1.82 A. Putting these

numbers into Eq. 3.6 gives us a value of the lattice energy of 759 kJ mol~!, which is quite close to the accepted value. Equation 3.6 makes it clear that the lattice energy is dominated by two

things: the charges on the ions and the ionic radii. A large lattice energy will result if the charges on the ions are large or the ions small. The Kapustinskii expression for the lattice energy is rather simple and we will find it very useful in the following examples. However, we should recognize that the values it gives will be quite approximate and so we must be

cautious about interpreting the results of our calculations in too detailed a way.

3.4

Applications

In this section we are going to look at two reactions in which trends can be

understood using calculated lattice energies.

Stabilization of high oxidation states by fluorine For many metals it has been observed that whereas the fluorides of high oxidation states are relatively easy to prepare, it is often the case that the other halides are more difficult or impossible to form. For example, CuF> 1s known, whereas attempts to prepare the corresponding copper (II) iodide have not been successful. Similarly, for cobalt in oxidation states III and IV, only the fluorides have

been prepared. The story is similar for manganese where for oxidation state II all of the halides are known but for oxidation state III only the fluoride has been prepared. There are numerous other examples of this tendency of high oxidation states only to be found as the fluoride.

3.4

Applications

29

It is thought that the difficulty in preparing these high oxidation state halides comes about due to the tendency for the halide to decompose into the lower oxidation state with the release of the halogen. For the case of an oxidation state III metal the reaction we are talking about is

MX3(s) —> MX2(s) + X(g)

(3.7)

where M is the metal and X a halogen. What we are going to do is to estimate the energy change for this reaction

and see what effect changing the halogen has. The analysis will be done using

the following cycle

A Haecomp

MX3(s) |

1

MX2(s) + 2X2(g)

A Fhattice (MX3)

_

8

—AH(M2+-M?3+)

M**(g) + 3X7 (g) ———

>

Fae

MX2)

| —Y2DO%2)

_

MP*(g) + 2X(g) + X(g)

Starting on the left the solid MX3 is dissociated into its constituent ions in the gas phase: the energy needed 1s the lattice enthalpy of MX3. The M?+ ion then gains an electron from one of the X~ ions to give M?+ and an X atom: the

energy needed is minus the third ionization energy of M, minus the electron affinity of X, EA(X). Finally, the M*+ and X7~ ions are recombined to form solid MX», for which the energy change is minus the lattice enthalpy of MX2, and the X atom recombines to form an X2 molecule, for which the energy change is minus half the dissociation energy of X2, D(X2). Overall, the enthalpy change for decomposition, A Hdecomp; 1S

A Haecomp =A Hiatice(MX3) — AH (M?7+ > ' MP*)

— EA(X) — A Mattice(MX2) — 2D(X2).

(3.8)

We can find the dissociation energies, ionization energies and electron affinities from tables. The lattice energies can be estimated using the Kapustinskii

formula, Eq. 3.6. For MX3, the number of ions, v, is 4, z+ = 3 and z— = 1, so the lattice energy is given by

A

MatticeMX3)/ lattice ( 3)/

1070x4x3x1

kJ mol!

(ry3+ + rx-)

=

12840

(ry3+ + rx-)

For MX2, v = 3, z4 = 2 and z_ = 1, so the lattice energy is given by A Aattice(MX2)/ kJ mol!

=

1070x3x2x1l (Tyq2+

+rx-)

_ (ryt

6420 +rx-)

We will complete the calculation for the specific case of cobalt, for which

the 3+ ion has a radius of 0.58 A, and the 2+ ion a radius of 0.71 A. These data

enable us to compute the required lattice energies and thus we can complete the calculation for all the halogens as shown in the table below.

Ionic interactions

30

1 2 3. 4

ry-/A AMhatice(CoX3) / kJ mol7! AH(Co** > Co3t+)/kJ mol7! EA(X7)/kJ mol7! AF hanice(COX2)/kJ mol7! * ~

5

%yD(X2)/kJ mol"!

6

AHéecomp / kJ mol7!

F Cl Br 1.98 1.82 1.33 5016 5350 6723 3238 = 332383238) —331 -—355 —334 2538 =. 2387 = 3147

I 2.20 4619 3238 —301 2206

79

121

112

107

592

-192

-—390

-—631

In accordance with Eq. 3.8, the value on line 6 is computed by subtracting

the values on lines 2 — 5 from that on line 1; these different contributions to AH decomp are visualized in Fig. 3.6. We see clearly from the table that the

decomposition reaction

(3.9)

CoX3(s) —> CoX2(s) + X2(g)

is exothermic for all of the halogens except fluorine. This provides a neat explanation as to why it is possible to prepare CoF3 but not any of the other trihalides as these can decompose to the lower oxidation state via an exothermic

reaction.

In this reaction there is certainly an increase in the entropy as a gas is

formed from solid reactants.

However, this favourable entropy change is un-

likely to outweigh the large positive enthalpy change in the case of the fluoride. For the other halogens, both the increase in entropy and the exothermicity im-

ply that the reaction will go to products. Just why it is that the fluoride is so different to the other halides can be

appreciated by looking at Fig. 3.6. What the diagram shows is that in compar8000

energy

/ kJ mol"!

6000 | 4000

F

|| |

2000 |}

wo IT -4000


M202(s) + O2(g).

We can analyse this reaction using the following cycle: 2MO2(s) |

AR, decomp

>

2A MMattice(MO2)

2M+(g)+20;(g)

M202(s) + O2(g) 8

——>

Fiase(M202)

|

2Mt(g)+057(g) + O2(g)

The quantity simply denoted x is the enthalpy change on going from the super-

oxide anion to the peroxide anion plus gaseous O2; for the present discussion we do not need to know its value.

Ionic interactions

32 The enthalpy change of the decomposition

AAgecomp,

reaction,

Can be

computed from:

(3.10)

A Adecomp = 2A Aattice(@MO2) + x — A Mattice(M202).

As before, we can use the Kapustinskii expression (Eq. 3.6 on p. 28) to estimate

hy >

the lattice energies:

A Miattice MO2)/ kJ mol” A Mattice(M202)/ kJ mol”

_;

_,

= =

1070x2x1xI1 ros) Oe 170x3x1x2 rae + ron)

2140 = tae + ros) = ue

6420 + roe)

Substituting these expressions into Eq. 3.10 we have

A Hdecomp

=

4280

6420

(rm+ + ror) 2A Miattice

(rm+ + ro2-) re

—

(MO)

/

A Matice(M202)

4

The radii of the O57 and O; ions are not that much different, so the quantity in the square bracket is negative on account of the larger numerator of the second fraction. Now imagine what happens as the size of the cation Mt is increased; both lattice energy terms decrease but the one for M2O2 decreases more than the one for MO? on account of the larger numerator in the second fraction. The term in the bracket therefore becomes less negative as the radius of the metal ion increases.

We therefore conclude that the trend is for the decomposition reaction of

the superoxide to become less favourable in energetic terms as the size of the

metal ion increases. This rationalizes the observation that the superoxide is not found for the early members of Group I, but 1s found for the elements toward the bottom of the group which have the larger ions. The argument here is not as detailed as in the previous example. We have not computed explicit values of the A Hgecomp for the different metals and then compared them with one another. Rather, recognizing from the first example that the variation in the lattice energies is usually the crucial factor, we have

simply looked at the way in which these terms will vary as the ionic radii are

changed.

3.5

lonic or covalent?

We mentioned at the start of this chapter that X-ray diffraction studies of crystals such as NaCl reveal that the electron density falls to a very low value between adjacent ions, and we cited this as evidence for the existence of ions

in such crystals. However, if we look more closely at the electron density in ‘ionic’ solids such as LiF, NaCl and KCI we find two things. Firstly, although the density between ions of opposite charge does become very low it does not

3.5

Ionic or covalent?

Fig. 3.7 Experimental electron density map for LiF determined using X-ray diffraction. The electron density is indicated by contours and the map shows the density in what would be a horizontal plane through the schematic structure shown in Fig. 3.1. Note that the electron distribution around the lithium is not spherical, which is taken as evidence of some covalent character in the bonding. (Reproduced, with permission, from H. Witte and W. Woelfel, Reviews of Modern Physics, 30, 53, (1958). Copyright (1958) by the American Physical Society.)

actually fall to zero. Secondly, the distance between the nucleus and the minimum in the electron density does not correspond to the tabulated value of the ionic radius. These two observations cast doubt on whether these solids really do contain ions in the way we have assumed.

Close inspection of the electron density map, such as the one shown in

Fig. 3.7 for LiF, reveals further problems. The contours of electron density around the lithium are not circular; if the lithium really was an ion its electron

density would be spherical and so the contours would be circular. This distortion is taken as evidence that the lithium is not truly an ion but that there is some sharing of electrons with the fluorine — in other words there is some covalent contribution to the bonding. Further evidence for there being some covalent contribution to the bond-

ing in these apparently ‘ionic’ solids comes from comparison of the calculated and experimentally determined values of the lattice energies (remember that such energies can be determined experimentally using a Born—Haber cycle). Whereas compounds such as NaCI and KI show good agreement between the

experimental and calculated values, for compounds of Ag(I) (e.g. AglI) and

Ti(1) (e.g. TIBr) the experimental lattice energy is significantly in excess of the

33

34

Ionic interactions calculated value.

As the calculation only considers the electrostatic contribu-

tion, this discrepancy is taken as indicating the presence of additional covalent contributions. In reality what we have is a continuum of types of bonding. At one extreme there is purely ionic bonding and at the other there is purely covalent bonding. Compounds such as LiF lie pretty close to the purely ionic end of the scale, whereas solids such as diamond and gsgphite are purely covalent . Everything

else lies in between and so will have both covalent and ionic contributions to the bonding; which is dominant is sometimes quite hard to decide! Unfortunately, all of this casts our lattice energy calculations into further doubt. However, we can continue to use these and to think about such solids as being ‘ionic’ provided that we realize that this is just an idealization and so treat our conclusions with some caution.

We now need to turn to the question of how to describe covalent bonding

which, along with ionic interactions, is the other important source of energy in

chemical reactions. As you know, it is the interactions between charged nuclei and electrons which are responsible for forming the covalent bonds which hold molecules together, so the first topic we must address is how to describe the behaviour of electrons in atoms and molecules. devoted to this subject.

The next three chapters are

4

Electrons in atoms

A chemical bond involves the sharing of electrons, so to understand how bonds are formed we need to understand where the electrons are and what they are

doing; we will start this process by first talking about electrons in atoms. You probably know quite a lot about this already and are used to describing the arrangement of electrons in an atom in terms of which orbitals are occupied.

Each orbital has a distinct energy and a particular shape, and we will see that when it comes to describing how bonds are formed these two properties are crucial. The material covered in this chapter is therefore vital to our under-

standing of chemical bonding.

The theory we need to describe the behaviour of electrons in atoms and

molecules is quantum mechanics.

We certainly do not have the space in this

book to go into the background and mathematical formulation of this theory.

Rather, we will simply introduce the key ideas and then present the results of quantum mechanical calculations in a pictorial way. This approach will bring us quickly and without too much effort to the really important points — the

shapes and energies of the orbitals.

Many of the ideas of quantum mechanics seem rather unusual, even counter-intuitive. This is because the world which we experience directly is governed by Newton’s Laws (classical mechanics) which are quite different

from the principles of quantum mechanics which apply to tiny particles such

as electrons. For the moment, we will simply ask you to accept the sometimes rather strange world of quantum mechanics. If you go on to study this in more

detail you will see where these ideas come from and how the predictions of the theory have been tested against experiments and found to be correct.

4.1

Atomic energy levels

One of the most important predictions of quantum mechanics is that the energy of an electron in an atom or molecule cannot take any value but is restricted to a specific set of values; the energy is said to be quantized. This prediction

blue

yellow

red

is entirely at odds with our direct experience of the world. For example, when

we ride a bicycle we expect to be able to go at any speed (that is, have any

kinetic energy). We do not expect to find that our speed, and hence energy, is restricted to particular values — but this is exactly what happens to the electron. Each allowed value of the energy is called an energy level, and we imagine that

a particular electron ‘occupies’ one of these levels. The most direct evidence for the existence of atomic energy levels comes from the study of atomic spectra, which involves measuring the wavelength of the light emitted by excited atoms. Such spectra show that light is only emitted at certain wavelengths, and that these wavelengths are highly characteristic of the atom being studied. Figure 4.1 shows part of such an emission spectrum

500

600 700 800 wavelength /nm

Fig. 4.1 Schematic emission spectrum from atomic sodium, such as would be seen by passing the light from a sodium discharge lamp through a prism or reflecting it off a diffraction grating. The most striking thing is that the emissions occur at a series of sharply defined wavelengths. in the case of sodium, the strongest by far is the yellow line at 589 nm.

Electrons in atoms

36

that the from sodium; such spectra are often called line spectra to indicate emissions are confined to a small number of well-defined wavelengths.

To understand how line spectra provide evidence of quantization of energy we first need to recall the relationship between the wavelength of light, A, and its frequency, v:

Av=c A

my

where c is the speed of light. Light can be thought of as being composed of photons whose energy, E, depends on their frequency in the following way: E=hv

where h is Planck’s constant.

It therefore follows that the energy and wave-

length of a photon are related by c E=h-. Xv

energy

+

photon

-—OFig. 4.2 Atomic emission spectra are produced when an electron (represented

by the circle) drops down from a higher energy level to a lower one. This releases a photon whose energy matches the

energy difference between the two levels. The energy of the photon therefore depends on the energy leveis in the atom

and the observation that only photons of specific energies are produced is taken to imply the existence of energy levels.

So, light of a particular wavelength corresponds to photons of a particular energy. Our interpretation of atomic line spectra is that an electron in an excited atom drops down from one energy level to another, releasing a photon whose

energy matches the difference in energy between the two levels (Fig. 4.2). As the photons emitted from a particular atom are at sharply defined energies, the

energies of the levels themselves must also have fixed values. If the electrons

in an atom were allowed to have any energy, any change in the energy of the electron would be possible and so light would be emitted at all wavelengths. The observation of atomic line spectra is thus direct evidence for the existence of atomic energy levels. Atomic orbitals

The energy levels which the electrons can occupy in an atom are called atomic

orbitals. The electronic configuration for an atom is generated by filling up the orbitals, starting from the lowest energy one and moving up in energy until all the electrons are used up; each orbital can accommodate two electrons, one

with spin ‘up’ and one with spin ‘down’. The lowest energy orbital is the Is, and this single orbital forms the first shell, or K shell. This shell can accommodate up to two electrons giving the possible configurations 1s! and 1s* which correspond to hydrogen and helium,

respectively.

The next in energy is the L shell, which contains the 2s orbital and the three 2p orbitals. Lithium (atomic number, Z = 3) has the configuration 15s*2s! and

neon (Z = 10), in which the L shell is full, has the configuration 15*2s22p°.

The next shell is labelled M@ and contains the 3s orbital, three 3p orbitals

and five 3d orbitals. The elements of the third row of the Periodic Table have electronic configurations which involve filling this shell. We

will see in the next section that we can use a special kind of spec-

troscopy to find direct evidence for the existence of these orbitals and to measure their energies. Then, in the following section, we will look more closely at just exactly what an orbital is and what is meant by the labels 2s, 3p, etc.

4.2

Photoelectron spectroscopy

4.2

37

Photoelectron spectroscopy

Photoelectron spectroscopy (PES) ing the energy levels of electrons recorded by irradiating the sample for the photons to ionize electrons

provides a particularly direct way of probin atoms and molecules. Such spectra are with light of a fixed frequency high enough from the sample; what we actually measure

are the energies of these ionized electrons. As energy is conserved, it follows

that

energy of photon = energy of ionized electron + ionization energy of that electron. So, the higher the energy of the ejected electron, the lower the ionization en-

ergy of the electron which has been ejected; the whole process is illustrated in Fig. 4.3. o

oe

22 2° =

3p —-—

3s

—O-

“a | 2p ~o— 25 —O—

+ (a)

Oo

“, —O—

OO

—° —O—

3s =O—

o7

(b)

2p—o— 35 —O—

—-O-

—

9.

7

—Q— —o—

ad

increasing electron energy has two bonding electrons, Hy has only one, so we might expect the bond in the latter to be weaker than in the former. Experiment bears this out: the

bond dissociation energy of Hy is 256 kJ mol~! whereas that of Hp is 432

kJ mol™!.

5.3

Symmetry labels

Ht

65

H,

Het

He,

Fig. 5.6 MO diagrams (as in Fig. 5.5) for a series of molecules with increasing numbers of electrons; the occupation of the orbitals by the electrons is indicated by the arrows. Occupation of the bonding MO favours the formation of a bond as it lowers the energy relative to the AOs; occupation of the antibonding MO has the opposite effect. These diagrams predict that HZ, Ha and Hes should be stable with respect to dissociation into atoms or ions whereas Hes should not form.

He? has four electrons, so we have to put two in the bonding MO and two in

the anti-bonding MO. Occupation of the bonding MO favours formation of the bond, but occupation of the anti-bonding MO disfavours formation of the bond.

Overall, the two effects cancel one another out and so there is no tendency for

the molecule to form as the energy is not lowered as the atoms come together.

Detailed calculations show that the anti-bonding MO

is raised in energy by

slightly more than the bonding MO is lowered, so if both are occupied equally the overall effect is to disfavour the formation of a bond. In agreement with our prediction, no He2 molecules have ever been observed experimentally.

Finally, Hey represents an interesting case. Here there are three electrons, two in the bonding and one in the anti-bonding MO. So, overall there is net bonding as the number of bonding electrons is greater than the number of anti-

bonding electrons. We therefore predict that the molecule He> should be stable with respect to dissociation into He + He*. Experiment confirms this prediction:

He;

290 kJ mol™!.

has been observed and found to have a dissociation energy of

This first application of the MO approach is very nice indeed — it gives us a simple and straightforward explanation of the bonding and occurrence of the molecules Hz, He2 and their ions. A ‘dot and cross’ picture of these molecules simply cannot explain what is going on — we need the MO approach.

5.3

(a)

Symmetry labels

MOs are given labels which tell us about their symmetry with respect to the molecule. For a diatomic, the first of these symmetry labels refers to what happens to the orbital when we traverse a circular path around the internuclear axis; this is illustrated in Fig. 5.7 (a). The circular path is centred on the bond

and is in a plane perpendicular to the internuclear axis. If, when we make a complete circuit of this path, the orbital does not change sign it is given the label o (‘sigma’). Looking at Fig. 5.3 on p. 63 we see that neither the bonding nor the anti-bonding MO has a sign change along such a

path, so they are both given the label 7. Sometimes we distinguish the antibonding orbital by adding a superscript star: a. If during a complete revolution we cross one nodal plane (i.e. a plane where the wavefunction is zero) the symmetry label is 2 (‘pi’). We will not encounter orbitals which have other than o or 7 symmetry.

WU

(b)

a b*

Fig. 5.7 Illustration of the two symmetry Jabels which are used to describe MOs in diatomic molecules. The first symmetry label refers to traversing a circular path around the internuclear axis, as shown in (a). If the wavefunction does not change sign along this path the orbital is given the label o. If the circular path crosses a nodal plane the orbital is given the label x. The second label, shown in (b), refers to what happens when we start at any point a, go in a line to the centre of symmetry of the molecule (marked with a dot) and then carry on an equal distance to point b. If the orbital has the same sign at a and b the symmetry label is g; if the sign has changed, the label is u. Note that the second symmetry label only applies to homonuclear diatomics.

Electrons in simple molecules

66

A homonuclear diatomic possesses a kind of symmetry called a centre of inversion, which is the point mid-way between the two atoms; the MOs can be classified according to their behaviour with respect to this kind of symmetry. The process is shown in Fig. 5.7 (b). We start at any point, a, and move in a straight line towards the centre of inversion; having reached the centre we carry on in the same direction for the same distance until we reach point b. If

the orbital has the same sign at points.q and b it is given the label g (for gerade,

‘even’ in German). From Fig. 5.3 on p. 63 we can see that the bonding MO has this g symmetry; this label is added to the o as a subscript: og.

If, on going from point a to b, the orbital changes sign we attach the label

u (for ungerade, ‘odd’ in German). We see from Fig. 5.3 that the anti-bonding

MO has this symmetry, and so it is given the label o, or a. The o and z labels can still be applied to MOs in heteronuclear diatomics,

but the g/u symmetry labels cannot as heteronuclear diatomics do not possess

a centre of inversion.

We sometimes also label the MOs with the AOs from

which they are derived, so for example the bonding MO in H2 can be labelled 1S Og.

5.4

General rules for forming molecular orbitals

We now want to move on to construct the MOs for molecules more complex than H2, so we need to consider what happens when there are more AOs present than just the two Is AOs in Hz. It turns out that there are some simple rules about how MOs are constructed from AOs; we will look at each of these rules

in turn.

Only AOs with similar energies interact to a significant extent

When two AOs interact to form MQs, the extent of the interaction 1s reflected in the amount by which the bonding MO goes down in energy, or equivalently the amount by which the anti-bonding MO goes up in energy. So, a large interaction results in the MOs differing significantly in energy from the AOs, whereas if there is little interaction the energies of the MOs are not much different from those of the original AOs.

When two AOs interact, it is always the case that the bonding MO is lower in energy than the lowest energy AO, and that the anti-bonding MO is higher

in energy than the highest energy AO. Figure 5.8 illustrates the effect on the MO energies of increasing the energy separation of the AOs. In (a) the AOs are matched exactly and the interaction is strong, as evi-

denced by the large drop in energy of the bonding MO when compared to the AOs. In (b) the match is not quite as good and we see that the drop in energy of the bonding MO is less; in (c) the mismatch is even greater and the fall in energy of the bonding MO is correspondingly smaller. Finally in (d) there is hardly any interaction and the bonding MO is more or less at the same energy as the lowest energy AO.

5.4

General rules for forming molecular orbitals

67

—=

(a)

(b)

(c) decreasing interaction

(d)

a

Fig. 5.8 Illustration of how the interaction between two AOs decreases as the energy match between them gets poorer; the downward pointing arrow gives the amount by which the bonding MO is lower in energy than the lower energy AO.

The size of the AOs is important The two AOs interact in the region where their wavefunctions overlap; the extent of overlap will depend on the size of the orbitals and how close together they can come. The size of an AO is determined by the principal quantum number and the effective nuclear charge, whereas how close two AOs can approach depends on the bond length. Generally what is found is that when considering the interaction between identical orbitals increasing their size decreases the degree of overlap. So, for example, two 3s orbitals overlap to a lesser extent than two 2s orbitals.

Similarly, we find that the overlap between a 2s and a 3s orbital is less than between two 2s orbitals.

AOs must be of the correct symmetry to interact

This condition is best illustrated by giving an example of a case where the two

AOs are not of the correct symmetry. Consider the case shown in Fig. 5.9 in which the overlap along the z-axis (the axis of the bond) of a 2p, orbital with

a ls orbital is depicted; recall that the 2p, orbital points along the x-axis, so it will point perpendicular to the z-axis. In (a) the orbitals are far apart so that

we can see Clearly the positive and negative lobe of the p orbital and the single positive lobe of the 1s orbital. 2p,

1s

(b)

region of

A

*

\

\.

constructive overlap

‘ad

region of estructive overlap

Fig. 5.9 Illustration of the symmetry requirement for AOs to overlap. (a) Shows a 2px and a 15 AO about to overlap along the z-axis; the positive parts of the orbitals are shaded grey. In (b) the overlap has begun, but we see that there is a region of constructive overlap (where the two orbitals have the same sign) and a region of destructive overlap (where the orbitals have opposite sign). These two regions cancel one another out leading to no net overlap. The black dots indicate the location of the nuclei.

As the orbitals come together, shown in (b), the positive lobe of the 2p orbital overlaps with the positive 1s orbital; this is the kind of constructive

overlap which leads to the formation of a bonding MO. However, the negative

Electrons in simple molecules

68

lobe of the 2p orbital overlaps with the positive Is orbital; this is the kind of destructive overlap which leads to the formation of an anti-bonding MO. In the case shown here the constructive and destructive overlaps exactly cancel one another out, leading to no net overlap. So, we conclude that the 2p, and Is orbitals do not have the correct sym-

metry to overlap along the z-axis. The same is true for the 2p, and Is orbitals. However, as is illustrated in Fig. 5.10,the 2p, and 1s orbitals do have the correct symmetry to overlap.

Fig. 5.10 In contrast to the case shown in Fig. 5.9, a 2pz orbital has the correct symmetry to overlap with a 1s AO along

the Z-axis.

When n AOs interact the same number of MOs is formed We have already seen an example of this when two AOs in H2 gave two MOs. In Chapters 6 and 10 we will see some examples of the interaction of more than two AOs.

5.5

Molecular orbitals for homonuclear diatomics

We will now use these rules to construct the MO diatomic molecules Liz, Bez,

diagram for the series of

..., Nez formed by the elements of the first row

of the Periodic Table. The first thing we need to think about is which AOs might overlap with one another; from our knowledge of the electronic configurations (b)

of these atoms we know that the relevant orbitals are the Is, 2s and 2p. In fact we need not consider the Is as they are so contracted towards the nucleus (due to the high effective nuclear charge they experience) that, as illustrated in

Fig. 5.11, they do not overlap to a significant extent. So, the only orbitals we need to consider are 2s and 2p.

Fig. 5.11 Illustration of why the 1s orbitals are not involved in bonding in diatomic molecules formed from elements of the first row of the Periodic Table. On account of the high effective nuclear charge experienced by the 1s electrons the orbitals are highly contracted and so, for typical bond lengths, they do not overlap to a significant extent, as shown in (a). In contrast, the 2s orbitals are much larger and so overlap well as shown in (b).

The 2s orbital is spherical, just like the Is orbital, but as we have seen (Fig. 4.18 on p. 46) the 2s has a radial node close in to the nucleus. However, this does not really affect the way

in which the 2s AO

overlaps with other

orbitals as the region of overlap is much further out than is this node. So, to all practical intents and purposes, we can simply treat the 2s as a spherical orbital. There will be a perfect energy match between the 2s AO on one atom and the 2s on the other, so we expect a strong interaction between these orbitals.

Similarly, the 2p AOs will have a perfect energy match.

However, as we saw

on p. 56 the 2s is lower in energy than the 2p, so the energy match between

these two orbitals is not perfect and therefore the interaction is not as strong as

between 2s and 2s or between 2p and 2p. Taking advantage of this effect we

will for now ignore any overlap between 2s and 2p when we construct our MO

diagram. We have already seen how two 1s AOs combine to give a o bonding orbital (og) and a o anti-bonding orbital (o,,); the same thing happens for the 2s or-

bitals and we will denote the resulting MOs 2s o, and 2s o,. The 2p orbitals

can overlap to give MOs of both o and z symmetry, as described in the next

section.

MOs from the overlap of p orbitals If we take the internuclear axis to be the z-direction, then two 2p, orbitals can overlap ‘head on’ to give 0 MOs as shown in Fig. 5.12 (a). The bonding MO

5.5

Molecular orbitals for homonuclear diatomics

(b)

|

|

(a)

69

OO

2po,

&>

apr,

Fig. 5.12 MO diagrams illustrating the formation of « and m type MOs from the overlap of 2p AOs. The ‘head-on’ overlap, shown in (a), leads to o MOs, whereas the ‘side-on’ overlap (b) leads to 7 MOs. The 2p AOs are drawn so that adding them together leads to constructive interference. The dots indicate the location of the nuclei.

is formed when there is constructive interference between the two lobes which face toward one another along the z-axis; as with the 2s 0 MO the concentration of electron density between the two nuclei is largely responsible for the lowering in energy of the MO. In Fig. 5.12 (a) the 2p orbitals are drawn so that simply adding them to-

gether gives constructive interference. The other combination we need to consider comes from subtracting the orbitals; this leads to destructive interference

and the formation of the anti-bonding MO in which electron density is pushed

away from the internuclear region.

It is important to realize that the way we choose to represent the 2p AOs is arbitrary; we could just as well have made the left-hand lobe on both AOs pos-

itive. With this choice, adding together the two AOs would lead to destructive

interference and the formation of the anti-bonding MO, whereas subtracting the two AOs would lead to the formation of the bonding MO. Either way, we

still end up with a bonding and an anti-bonding MO. Figure 5.13 shows surface plots of the two MOs and Fig. 5.14 shows con-

tours plots of the same orbitals. The two MOs are centre of inversion the bonding MO has symmetry has symmetry u. We therefore denote the orbitals their symmetries and that they are derived from 2p

both o; with respect to the g and the anti-bonding MO 2p og and 2p o, to indicate orbitals.

The 2p, and 2py AOs point in directions perpendicular to the internuclear

axis and, as was discussed on p. 67, these orbitals do not have the correct

symmetry to overlap with the 2s orbitals. A similar line of reasoning, illustrated

in Fig. 5.15, shows us that a 2p, on one atom cannot overlap with a 2p; on the

other. However, the two 2p, AOs can overlap ‘side on’ in the way illustrated in

Fig. 5.12 (b); the shapes of the resulting orbitals are best appreciated from the

surface and contour plots shown in Figs. 5.16 and 5.17.

Constructive interference leads to a bonding MO in which there is electron density above and below the internuclear axis; note the contrast to ao bonding

MO which has electron density directly between the two nuclei.

Electrons in simple molecules

Ss

ZB

‘7

70

2p o,, bonding MO

2p o,, anti-bonding MO

Fig. 5.13 Surface plots of the 2p og (bonding) MO and the 2p ay (anti-bonding) MO formed from the head-on overlap of two 2p orbitals. Note how the bonding MO concentrates electron density in the internuclear region whereas the opposite is true for the anti-bonding MO. The two nuclei are placed along the z-axis, symmetrically about z = 0.

‘

.

‘

5

‘

*

-7 \5 ‘ a!vos ‘.

7

ii

so?

i

:

!

:

:

.

:

i :

:

:

:i H if{ H an) , ON *

5

‘

:

errr

H :‘

mS sae

! : H

‘‘ 7

'

é

¢

VA

:H age o= SAN yt we NNN : a iat \ \ ‘ : ' ! Pals titan Ha Tre Oe PTS

:

i

z

a

aft

Soar

‘ “eee”

2p a, bonding MO

2p o,, anti-bonding MO

Flg. 5.14 Contour plots of the 2p ag (bonding) MO and the 2p ay (anti-bonding) MO. The cross-section shown is the xz-plane (with z running horizontally); the positions of the two nuclei are indicated by the small black dots.

This difference in the electron distribution explains why the MO formed by the side-on overlap is less strongly bonding than the o bonding MO. Sideon destructive interference leads to an anti-bonding MO in which the electron

density is pushed away from the region above and below the internuclear axis. Both the bonding and anti-bonding MOs have a nodal plane which contains the two nuclei. In addition, the anti-bonding MO has a second nodal plane

2p,

2p,

Fig. 5.15 Illustration of why a 2pz AO and

a 2px AO have no net overlap; the region of constructive interference is balanced out by the region of destructive interference, just as in Fig. 5.9 on p. 67.

which lies between the two nuclei, perpendicular to the internuclear axis.

Inspection of Fig. 5.16 shows that the symmetry is 7 as when traversing a circular path perpendicular to the internuclear axis (see Fig. 5.7 (a) on p. 65) we cross a nodal plane. The bonding orbital has u symmetry and so is given the full label 2p 7, and the anti-bonding orbital is g so is given the label 2p z,.

The two 2py AOs can also overlap with one another to give two more 7 MOs, one bonding and one anti-bonding. So, there is a total of two bonding x orbitals and two anti-bonding z orbitals: one bonding and anti-bonding pair

5.5

Molecular orbitals for homonuclear diatomics

2p t,, bonding MO Fig. 5.16 Surface plots of the 2p xy side-on overlap of two 2px orbitals. anti-bonding MO also has a nodal axis. Note that for the bonding MO and below the internuclear axis. The

2p Tg anti-bonding MO (bonding) MO and the 2p zg (anti-bonding) MO formed from the Both MOs have a nodal plane containing the two nuclei, and the plane between the two nuclei, perpendicular to the internuclear there is a concentration of electron density in the regions above two nuclei are placed along the z-axis, symmetrically about z = 0.

2p r,, bonding MO

2p Ng anti-bonding MO

Fig. 5.17 Contour plots of the 2p zy (bonding) MO and the 2p 7g (anti-bonding) MO; the nodal planes are clearly visible in both piots. The cross-section shown is the xz-plane (with z running horizontally); the positions of the two nuclei are indicated by the small black dots.

lie in the xz-plane and the other pair lie in the yz-plane. The two bonding MOs are degenerate, as are the two anti-bonding MOs.

Two MO diagrams for the Az molecules If we consider only the 2s-2s and 2p-2p overlap it is quite easy to assemble

the complete MO diagram, which is shown in Fig. 5.18 (a). On the left and right are shown the AOs, with the 2s lower in energy than the 2p. The three degenerate 2p orbitals are represented by the three closely spaced lines labelled

2p on the diagram. The 2s orbitals overlap to form a bonding MO, 2s og, and an anti-bonding MO, 2s 0,. The 2p orbitals which point along the bond (the z-direction) also

overlap to form o orbitals: 2p a, (bonding) and 2p o, (anti-bonding). The two 2p, orbitals overlap to give a 77 bonding MO (2p 7) and a 7 anti-

71

Electrons in simple molecules

72

2po,

———.

20

2pn,,

9 ii

In,

2p,

_

20,

256,

——.

10,

1o,; 25 —_—

lo,

‘

AOs on atom 1

2s

2s Oy AQOs on atom 1

‘

_—__.

MOs

AOs on atom 2

; 16, MOs

AQs on atom 2

Fig. 5.18 Shown in (a) is a simple MO diagram for the homonuclear diatomics of the first row, constructed by considering only 2s-2s and 2p-2p overlap; this diagram turns out to be appropriate for O2 and Fo. However, for the molecules Lia...., No the MO diagram is of the form shown in (b). The difference between (b) and (a) is that the s and p orbitals are much closer in energy in (b) so that we need to include the effect of s-p mixing; this results in a re-ordering of the x and o bonding orbitals derived mainly from the 2p AOs. The MOs in diagram (a) are labelled according to which AOs each MO is derived from; diagram (b) is labelled using a different scheme in which orbitals of the same symmetry are simply distinguished from one another by numbering them 1, 2, ...; the MOs in diagram (a) are also labelled using this second scheme.

bonding MO (2p zz). The same is true of the two 2py orbitals, so there are two degenerate 2p m, orbitals, indicated by the two closely spaced lines, and two

degenerate 2p mg orbitals indicated in the same way. Generally o interactions are stronger than 7, so we have shown the 2p oy as being lower in energy than

the 2p my. Right at the start of this section (p. 68) we made the assumption that the 2s and 2p orbitals are far enough apart in energy that we do not need to consider’

the possibility of o overlap between them. Therefore, the MO diagram shown in Fig. 5.18 (a) is only suitable for cases where this assumption is appropriate. We saw in Fig 4.34 on p. 57 that the energy separation between the 2s and 2p increases as we go across the first row of the Periodic Table. It turns out that this separation is sufficient in oxygen and fluorine for the MO diagram of Fig. 5.18 (a) to be correct.

However, for the other elements (Li, ..., N), the

separation of the 2s and 2p is such that we cannot ignore the effect of o overlap between these AOs.

5.5

Molecular orbitals for homonuclear diatomics

73

The most significant effect of these s-p interactions (usually called s-p mixing) is to make the 2p og MO less bonding (i.e. to raise its energy) and the 2s

oy, MO less anti-bonding (i.e. to lower its energy). For the elements Li, ..., N the shift of the 2p og is large enough to move it above the 2p m, MO, as is shown in Fig. 5.18 (b). When there is significant s-p mixing we cannot really label an orbital 2p og

as it is not correct to identify it as being derived solely from 2p; the symmetry

labels o and g are still applicable, though. Under these circumstances we drop

the 2p prefix and simply number the orbitals to distinguish ones with the same symmetry, so the first og MO is labelled lo, and the second 20. The other orbitals are labelled using a similar scheme, as is shown in Fig. 5.18 (b); the same scheme can be used to label the orbitals in MO diagram (a).

Using the MO

diagram

We can now use the MO diagrams of Fig. 5.18 to make some predictions about

the homonuclear diatomics of the first row. All we have to do is to slot the appropriate number of electrons into the MOs and then work out what are the

consequences of the resulting electronic configuration. For example, lithium has the configuration 1s?2s!, but as we commented

on before, the 1s electrons are not really involved in bonding, so we need only

be concerned with the single 2s electron. The electrons which are involved in bonding are called the valence electrons, and there are two of these in Lio. For this molecule the appropriate MO diagram is Fig. 5.18 (b) and so the two valence electrons go spin paired into the lo, orbital giving the electronic configuration lo. We can carry on in the same way for the diatomics Liz, ..., N2, giving the results shown in the table below (a star has been added

to indicate the anti-bonding MOs).

The table also shows the bond order, the

meaning of which we will come on to shortly.

log | lo,

lr,

202

Im,

bond order

Liz | tl

1

Be2 | th | tl

0

Bo;

th | th | tft

|

No}

tH | th

QIN

| tinh

| th

th |] ty

2 3

In Liz both electrons are in a bonding orbital and there are no electrons in

anti-bonding orbitals, so we predict that the molecule is stable with respect to dissociation into atoms. Experiment bears this out: molecular Liz has been observed in the gas phase and it is found to have a bond dissociation energy of 101 kJ mol~!. The two electrons in a o bonding MO create a o bond between

the two atoms, so the molecule is described as having a single o bond.

In Be» there are two electrons in a bonding MO and two in an anti-bonding MO; the simple expectation is that the molecule has no net bonding and so will

Electrons in simple molecules

74

the not form (just as was the case for He2). In fact, because of the s-p mixing, lo, orbital is somewhat less anti-bonding than the log is bonding, so overall

Be? is expected to be a weakly bound species. The molecule has been observed

in the gas phase and is found to have a rather low dissociation energy of 59

kJ mol7!.

B> has six valence electrons; four of these are spin paired in o orbitals and the last two go into different 17, orbitals with their spins parallel. Remember

that when there are degenerate orbitals the lowest energy arrangement for two

electrons is to put them into separate orbitals with their spins parallel.

There is a special feature of Bz which we can explain using the MO dia-

gram, which is that the molecule is found to be paramagnetic.

Paramagnetic

substances are drawn into a magnetic field — an effect which can be measured

experimentally.

Paramagnetism is associated with the presence of unpaired

electrons, which, according to the MO diagram, is precisely what we have for B>.

The bonding effect of having two electrons in the log is roughly cancelled

out by having two electrons in the anti-bonding 1o,, so the bonding in Bz is mainly due to the two Iz, electrons. A useful way of expressing the degree of bonding is to calculate the bond order, which is given by bond order =

Y

[number of bonding electrons — number of anti-bonding electrons] .

The factor of one-half is included so that a pair of bonding electrons, which we think of as comprising In the case of Liz (2 — 2) = 0. These bond and Be? having order in Bz is (2 — the values of the bond

a bond, gives a bond order of one. the bond order is (2 — 0) = 1, whereas for values fit in with the description of Liz having (to a first approximation) no bond. Similarly 2+ 2) = 1, i.e. a single bond. The table on p. order for each molecule.

Be? it is a single the bond 73 gives

The bond order is a rather rough measure of the degree of bonding as it

takes no account of the relative contribution to the bonding of different bond-

ing orbitals (and similarly for anti-bonding MOs).

However, there is quite a

good correlation between the bond dissociation energy (a measure of the bond strength) of the molecules Az and the bond order, as shown in Fig. 5.19. The next diatomic is C2 which has eight valence electrons. These fill the log, the lo, and both of the 17, orbitals with all spins paired; the result is

two mz bonds. N2 has 10 valence electrons and these occupy the MOs in such a way that there are two wz bonds and one o bond; this is consistent with the simple view that N2 has a triple bond and indeed the bond order is 3.

This

molecule has the largest bond order of all of the diatomics of the first row and So is expected to have the strongest bond, which is indeed the case. Once we get to oxygen and fluorine the appropriate MO diagram is Fig. 5.18 (a) which has a different ordering of the orbitals. The electronic

configurations for these last two diatomics are therefore:

5.5

Molecular orbitals for homonuclear diatomics

7

1000

~

800F

2

75

*N,

3 D 5 | 600-

°C,

iS

°0,

@ | 400F 3

8

°B,

55 200F

Fg7 eLi

Qa

(a)

2

lL

l

l

1

2

3

bond order _

Fig. 5.19 Plot showing the correlation between order for the homonuclear quantities.

log

bond dissociation energy (bond strength) and bond

diatomics of the first row.

| loy | 20%

Q|/

NW)

N]

Fo;

th | TL

Nit |

TL | TY

There is a useful correlation between these two

lx,

1%,

wit Oth | tL

bond order

t

2

OTN

1

In O all of the bonding MOs have been occupied and so the final two electrons have to go into the z anti-bonding MOs. As is the case for B2 the last two electrons are split between two degenerate orbitals with their spins parallel, making the molecule paramagnetic — which is what is found experimentally. In F the 7 anti-bonding orbitals are now full, so the net bonding is simply

from the 20, orbital. Finally, the hypothetical molecule Nez has all of the bonding and anti-bonding orbitals filled and so is not expected to form. The MO approach is remarkably successful at explaining the properties of the Az molecules.

Using it, we have been able to rationalize the variation in

bond strengths, explain why Bez and Nez are not expected to form, and predict

the observed paramagnetism of Bz and O2. We can be well satisfied with this

outcome! Figure 5.20 shows a plot of the energies of the occupied MOs for the homonuclear diatomics of the first period. We see that in general the energies of the MOs fall steadily across the period; this has the same origin as the fall in the orbital energies of the atoms, i.e. it is due to the increasing nuclear

charge — see Section 4.8 on p. 57. For B> and C2 the highest occupied MO is the 17, showing that this lies

lower in energy than the 20¢. In contrast, for Oz and F2 the 20 lies lower than the I7,,. For Nz these two MOs are rather close in energy and there is some uncertainty over their ordering.

Electrons in simple molecules

76

Be,

Li, 1o

g

16

we.

C,

Bs

Np

In :a

0»

Fe

In,

26

"

Fig. 5.20 Plot showing the calculated energies (to scale) of the occupied MOs for the homonuclear diatomics of the first row; the dashed lines connect similar MOs. Note that there is a general fall of the energies of the MOs as we go across the period and that for O2 and F2 the 2og lies below the 1zu.

5.6

Heteronuclear diatomics

The bonding in heteronuclear diatomics (ones in which the two atoms are dif-

ferent) can be described in a similar way to that used for homonuclear di-

atomics. There is one significant difference which is that there will no longer

be an exact match between the energies of the AOs of the two atoms; this makes it more difficult to construct the MO diagram as we have to decide which AOs will overlap. We will also see that this energy mismatch between AOs leads to

polarized bonds.

On p. 66 and in Fig. 5.8 it was explained that when the energy separation between two AOs becomes larger the interaction between them decreases. A further consequence of this energy mismatch is that the contribution of the two AOs to the MQs is not the same: this is illustrated in Fig. 5.21.

Figure 5.21 (a) shows the situation in which the two AOs have the same energy. The bonding MO has equal contributions from the two AOs, and the same is true of the anti-bonding MO except that the orbitals are combined with opposite coefficients. When the two AOs have different energies what we find is that the AO which jis closer in that MO. This is illustrated in (b) to the AO of atom 2 and so this contrast, the anti-bonding MO is so this is the major contributor to

energy to the MO is the major contributor to in which the bonding MO is closest in energy AO is the major contributor to the MO. In closest in energy to the AO from atom | and the MO.

As the energy mismatch increases further the relative contributions of the

two AOs to a given MO become even more unequal, as is shown in Fig. 5.21 (c). Now the bonding MO has a much larger contribution from the AO on atom

2 than from that on atom 1, and vice versa for the anti-bonding MO. If the bonding MO of Fig. 5.21 (c) is occupied the electron distribution will be uneven across the molecule, simply because the orbital (wavefunction) is greater in the region of atom 2 (recall that the electron density is proportional to

5.6

Heteronuclear diatomics

77

increasing orbital energy mismatch Fig. 5.21 {llustration of the effect on the MOs of increasing the energy mismatch between the two interacting AOs. In (a) the two AOs have identical energies, and so contribute equally to the bonding and anti-bonding MOs; this is shown in the cartoons of these orbitals where the MO is drawn such that the size of the constituent AO indicates its relative contribution. !f the energy of the AO on atom 2 is tower than that of atom 1, as shown in (b), the AO on atom 2 is a more significant contributor to the bonding MO whereas the AO on atom 1 is the more significant contributor to the anti-bonding MO. As the energy mismatch between the AOs becomes greater, the effect is more pronounced, as is shown in (c).

the square of the wavefunction). As a consequence, the bond will be polarized

towards atom 2, with a partial negative charge on atom 2 and a partial positive charge on atom 1. The bond will have a dipole moment, as shown in Fig. 5.22.

It is clear from this discussion that the relative energies of the AOs are important as this determines which will overlap most effectively and the polarity of any resulting bonds. In Section 4.8 on p. 57 it was described how the energies of the AOs decrease as we go across the first row of the Periodic Table. We can therefore use this observation to work out which of any two atoms has

—e’

e-

the lowest energy orbitals and hence draw up an appropriate MO diagram.

In Fig. 5.22 the AO from atom 2 is lower in energy and so the bond is polarized towards this atom. If we were describing this polarization in terms of electronegativities we would say that atom 2 is more electronegative than

HAOs lies between that of the 2s and 2p but closer to 2p than 2s, as shown in Fig. 6.7. Ammonia

and water

The sp* hybrids can also be used to give an approximate description of the bonding in ammonia (NH3) and water (H20). Ammonia is best described as being trigonal pyramidal, a shape which we can imagine as being derived from tetrahedral methane simply by ‘removing’ one of the hydrogens, as shown in Fig. 6.8. This gives us the clue as to how to describe the bonding in ammonia: we form four sp> hybrids on the nitrogen and let three of these overlap with

hydrogen 1s AOs to form three 2c-2e trons, so we assign the final pair not hybrid, classifying it as a lone pair. Of course there is a problem with bond angle in ammonia is 106.7° —

bonds. Ammonia has eight valence elecused for the N-H bonds to the fourth sp?

1 o——

%

Just as the energies of MOs are different from those of the AOs from which they are formed, the energies of the HAOs are different from the AOs which

2s

AQs

HAOs

Fig. 6.7 Illustration of the relative energies of the sp? HAOs and the AOs from which they are formed. Note that the three 2p orbitals are degenerate, but are shown slightly separated on this diagram;

the same is true of the four sp? HAOs.

this description, which is that the H-N-H not the same as the tetrahedral angle of

109.5° between the sp? hybrids. The difference is small, however, so our description is not far from the truth and we will see later on how to refine the model to produce the correct bond angle. The same approach can be used for water; we imagine its structure as being

derived from methane with two of the hydrogens removed. As before, we form

four sp* hybrids on the oxygen, and overlap two of these with the hydrogens to

form two 2c-2e bonds. The remaining four electrons are assigned to the other two sp® hybrids, forming two lone pairs. Once again, the experimental bond

Fig. 6.8 The structures of ammonia and water can be thought of as being based on the tetrahedral shape of methane with one and two of the bonds to hydrogen being removed, respectively.

angle of 104.5° does not quite match the angle between the sp> hybrids, but it

is pretty close. These

sp>

hybrids

are

not only

useful

for describing

the

bonding

in

methane, but also give us a start in describing the bonding in other molecules. In these we not only use the hybrids to form bonds but also use them to accommodate lone pairs. We will now turn to how other hybrids can be formed which point at different angles to the tetrahedral arrangement of sp° hybrids.

Other kinds of hybrid atomic orbitals The molecule BH3 has a trigonal planar shape in which the three hydrogens lie

in a plane and at the corners of an equilateral triangle with the boron at its centre (Fig. 6.9). Clearly the sp? hybrids are not going to be useful in describing the

bonding in this molecule — in fact what we need are the three equivalent sp” hybrids which are formed from the 2s and two of the 2p AOs. These hybrids are

depicted in Fig. 6.10 along with the remaining 2p, orbital which is not involved in forming the hybrids (the choice of the remaining orbital as pointing along z is arbitrary). Each sp” hybrid overlaps with a hydrogen 1s AO to forma bonding and an anti-bonding MO; a pair of electrons is assigned to each bonding MO, creating

H—Bx ~wHH Fig. 6.9 BHg is a trigonal planar moiecule; all the atoms lie in a plane,

with the hydrogens at the corners of an equilateral triangle.

Electrons in larger molecules

86

(not involved in hybridization) Flg. 6.10 Surface plots of the three equivalent sp” hybrids formed from the 2s, 2px and 2py AOs; also shown is the 2pz AO which is not involved in the hybridization. The three hybrids point at 120° to one another and all lie in the xy-plane.

three 2c-2e bonds.

BHs3 has six valence electrons, so there are just enough

for these three 2c-2e bonds. The remaining out-of-plane 2p, orbital is not occupied, but we will see later on that this orbital plays an important role in the chemical reactions of BH3. The complete MO diagram is shown in Fig. 6.11. We can also form hybrids of 2s with just one 2p (arbitrarily chosen to be

the 2p,) to give two equivalent sp hybrids; these are depicted in Fig. 6.12 along =.

2p =

weeeaes 2p,

i

i

= ” spr’. 25——" AOs

4

:

1s

;

greater the proportion of s-character in the HAOs the larger the angle between

= HAQOs

MOs

AOs

Fig. 6.11 MO diagram for BH3; on the left are shown the AOs of boron combining to give three sp? hybrids and leaving the 2pz orbital unhybridized. The three HAOs overlap one-on-one with the three hydrogen

with the two unhybridized 2p orbitals. The sp hybrids point at 180° to one another. A pattern now emerges: the angle between the sp* hybrids is 109.5°, between the sp* hybrids it is 120° and between the sp hybrids it is 180°. The

1s AOs shown on the right.

The molecule has six valence electrons which occupy the three bonding MOs; the 2pz is empty.

them. Put the other way, the greater the p-character the smaller the angle between the hybrids. So, by altering the ratio of s to p in our HAOs we can alter the angle between them. When we combined the 2s with the three 2p AOs we described the result-

ing sp? hybrids as equivalent, which means that each has the same ratio of s-

and p-character; this is why they all have the same angle between them. How-

ever, if we increase the s-character in one of the hybrids and proportionately decrease the amount of s-character in the other three, we expect to decrease

the angle between the orbitals which have lower s-character (and hence greater p-character). There are still four HAOs, but they are no longer equivalent. This set of inequivalent hybrids is just what we need to describe the bond-

ing in ammonia. The three hybrids with increased p-character are used to form the bonds to the hydrogens and the fourth hybrid (the one with greater s-character) accommodates the lone pair. Similarly, to describe the bonding in

6.2

Hybrid atomic orbitals

2p, AO (not involved in hybridization)

87

2p, AO

(not involved in hybridization)

Fig. 6.12 Surface plots of the two equivalent sp hybrids formed from the 2s and 2pz AOs; also shown are the 2px and 2py AOs which are not involved in hybridization. The two hybrids point at 180° to one another, and the unhybridized 2p orbitals point in perpendicular directions to the two hybrids.

water, we increase the p-character in two of the hybrids until the angle between

them is the required 104.5° and use these to form the 2c-2e bonds. The remaining two hybrids (which have increased s-character) are used to accommodate the two lone pairs.

The idea that the proportion of s and p AOs in the hybrid atomic orbitals

can be varied in order to account for different bond angles is nicely illustrated by the inversion of ammonia. The inversion of ammonia

H

Although the equilibrium geometry of ammonia is trigonal pyramidal it turns

the NH bond angles start to open out until the molecule becomes planar. One

way of describing what has happened is to say that the three hydrogens have

moved from a plane below the nitrogen into a plane containing the nitrogen.

The process then carries on with the three hydrogens moving to a plane above

His

ee

Y

y|

H

fie

trigonal pyramidal

HH

planar

ae

H tty

H

i

trigonal pyramidal

energy

out that this molecule constantly undergoes a process called inversion by which it is pulled ‘inside out’ like an umbrella on a windy day (Fig. 6.13). The molecule starts in its lowest energy geometry (a trigonal pyramid) and then

H

the nitrogen as the bond angles return to their equilibrium values. We regain the original geometry but with the hydrogens on the other side of the molecule compared to where they started from.

Fig. 6.13 Ammonia undergoes an inversion in which it turns ‘inside out’ by passing from the equilibrium trigonal

We have already described the bonding in ammonia as being based on sp? hybridization, but with the lone pair occupying.a hybrid of greater s-character. The planar form of NH; can best be described as having sp~ hybridization at

and then continuing to a trigonal pyramidal geometry which is the mirror image of the original. The energy is a

the nitrogen. These three hybrids overlap with the three hydrogen 1s orbitals,

and a total of six electrons are assigned to the resulting bonding MOs.

The

pyramidal geometry to a planar geometry

maximum

at the planar geometry and at

this point is 24 kJ mol above the

energy at the equilibriurn geometry.

Electrons in larger molecules

88

remaining pair of electrons is assigned to the out-of-plane 2p, AO. So, as the inversion proceeds we have an interesting progression of bonding. To start with the lone pair is in an sp type HAO with more s-character; as

the inversion proceeds the p-character of this HAO increases reaching 100% at the planar geometry. At the same time, the HAOs involved in bonding to the

hydrogens decrease in p-character as they move from sp? to sp”. Then, as the trigonal geometry is regained on the other side, the s-character of the lone-pair orbital increases and that of the HAOsjnvolved in bonding decreases.

Tetrahedral ions The ionic species NH7 and BH; are both tetrahedral and have eight valence electrons each.

For the case of NHj

the electron count is five from nitrogen,

four from the four hydrogens and —1 for the positive charge giving a total of 8. For BH; we count three from boron, four from the four hydrogens and +1 for the negative charge, giving a total of eight. To describe the bonding for both ions we form four equivalent sp° hybrids

on the central atom and allow these to overlap (one-on-one) with the drogen 1s AOs. Placing two electrons in each bonding MO uses up electrons to form four 2c-2e bonds. We might ask on which atom the charge is located: from the MO is clear that the charge cannot be associated with any one atom, but around all of the bonds. This is an important point which we will when considering the reactions of these two species.

6.3

four hyall eight

picture it is shared return to

Using hybrid atomic orbitals to describe diatomics

Hybrid atomic orbitals can be used to describe the bonding in diatomics and sometimes this results in a more convenient description than the full MO treat-

ment which we gave in Chapter 5. We will describe just one example: N2. We start out by supposing that the nitrogen is sp hybridized, with the hybrids pointing along the direction of the internuclear axis (z). The two sp HAOs

which point towards one another overlap to form o bonding and anti-bonding MOs; we place two electrons in the bonding MO. The other two HAOs which

point away from the bond are occupied by two lone pairs.

There are two sets of out-of-plane p orbitals: the two 2p, orbitals overlap to

give a

bonding MO and a corresponding anti-bonding MO; the two 2py AOs

overlap in the same way. Two electrons are placed in each of the 7 bonding MOs, using up all 10 valence electrons. Our description of the bonding in N2 is that there is a o bond and two m bonds between the nitrogen atoms; in addition each atom has a lone pair, which is directed away from the internuclear axis. The picture is summarized in Fig. 6.14. In fact, this picture is not too dissimilar to the MO description of the bonding in N2 given on p. 74 (see the MO diagram of Fig. 5.18 (b) on p. 72). In the MO picture the s-p mixing causes the 1a, MO to become less anti-bonding

and the 2a¢ orbital to become less bonding; it turns out that occupation of these

orbitals contributes rather little to the net bonding so they can be described as

6.4

Simple organic molecules

89

On@@ro 6 bonding MO

N——On@ F sp lone pair

x

e

©

N ne

N C)

m bonding MO from 2p, y

eS

C)

N

N

es

eu

sp lone pair

m bonding MO from 2p,

Fig. 6.14 Cartoons showing a description of the bonding in No using sp hybrids. Two of the hybrids overlap to form a o bonding MO and the remaining two hybrids become lone pairs. A x bonding MO is formed from the overlap of the two 2px AOs,

and similarly another x bonding

MO

is formed

from

the overlap of two 2py AOs. In these terms, the description of No is of a « bond, two x bonds and two lone pairs. Note that for the a overlap of the two sp hybrids the lobes of the HAOs are shown with the signs that will lead to the bonding MO; do not forget, though, that an anti-bonding MO will also be formed. The same applies to the x overlap which gives a bonding and an anti-bonding MO.

approximately non-bonding. It is the occupation of the log MO (two electrons) and 27, MOs (four electrons) which is responsible for most of the bonding in

N2; in other words there is a o and two in Fig. 6.14.

6.4

bonds just as in the description given

Simple organic molecules

Hybrid atomic orbitals are a very convenient way of simple organic molecules so in the following chapters very often. Generally, it is clear from the structure should use for a particular carbon: if the coordination hybrids, if the carbon is doubly bonded we need sp”

describing the bonding in we will use this approach what kind of hybrids we iis tetrahedral we need sp* hybrids and if it is triply

bonded we need sp hybrids. For other atoms, such as nitrogen and oxygen, the

choice is sometimes less clear and we will discuss this later on in this section.

First, however, we will look at the description of the bonding in three simple

hydrocarbons. Ethane, ethene and ethyne

In ethane, C2H¢, both carbons are tetrahedral and so it is clear that we should use sp? hybrids to describe the bonding. Of the four hybrids on each carbon,

one overlaps with a hybrid on the other carbon and the other three overlap with hydrogen Is orbitals. Each overlap is just between two orbitals and results in a a bonding and ao anti-bonding MO. We put two electrons in each bonding

sp*-sp* H

seis

"NS, —

|/

H d

\" 4

MO thus forming a 2c-2e bond; the overall picture is summarized in Fig. 6.15. There are 14 valence electrons in ethane (four from each carbon and six from

Fig. 6.15 Schematic structure of ethane

Ethene, C2H4, is flat with 120° H-C-H and H-C-C bond angles; the choice of sp” hybrids for the carbons is therefore clear. The bonding in this molecule

either two sp? hybrids (for the C-C bond) or an sp® hybrid and a 1s AO on

the hydrogens), and these fill all of the

a bonding MOs.

separates into two parts: firstly, a o framework which involves the sp” hybrids

in which each line represents a 2c-2e

bond. Each bond can be described as being the result of the overlap between

hydrogen (for the C~H bonds).

Electrons in larger molecules

90 sp?-sp* H \

eis

" NY

o framework Fig. 6.16 The bonding in ethene hybrids on carbon and 1s AOs framework. The out-of-plane 2p do not forget that there will also

@ "OF

Hing

/

~

Cc wth

m system on o framework

; ty can be separated into a o framework, involving the overlap of sp* on hydrogen, and a x system which lies out of the plane of the a orbitals are shown with the signs that lead to the 7 bonding MO, but be a w anti-bonding MO formed by the destructive overlap of these

two 2p orbitals.

and the 1s AOs; secondly, the 2 bonding between the two carbons. The o framework is much the same as that for ethane with the single exception that sp”, rather than sp?, hybrids are involved. For the C-C bond, two sp?

hybrids overlap to give o bonding and anti-bonding MOs; for the C-H bonds the overlap is between an sp* hybrid and a hydrogen 1s orbital. Filling all of these o bonding MOs accounts for 10 electrons. Pointing out of the plane of the molecule are the two 2p, carbon AOs which were not involved in the hybrids (see Fig. 6.10 on p. 86). These two orbitals

overlap to give az bonding and a z anti-bonding MO. Assigning two electrons to the bonding MO accounts, together with those in the o framework, for all of the 12 valence electrons in ethene (four from each carbon and four from the hydrogens). Figure 6.16 summarizes the picture of the bonding which we have

developed: the two carbons are joined by ao bond and a z bond, forming the double bond which we expect for ethene. This diagram also explains a marked difference between ethane and ethene. Whereas in ethane there is quite a small energy barrier for rotation about the C-C bond, in ethene a great deal of energy is needed to rotate about the double bond — so much that we can safely regard it as being fixed. The easy rotation

about the single bond in ethane comes about because the bond is formed by aa MO in which the orbitals overlap head-on. Rotation about the bond axis makes no difference to the overlap, and so does not affect the bonding.

In contrast, forming the z bond in ethene requires that the two 2p AOs lie in the same plane, as shown in Fig. 6.16. Rotating about the C-C axis will

result in the loss of this overlap, thus breaking the 2 bond; this is why rotation about this bond needs so much energy. Finally, we come to ethyne (acetylene), C2H2, which is a linear molecule;

sp hybridization at the carbons is therefore appropriate, giving the bonding scheme illustrated in Fig. 6.17. As with ethene, we can separate the bonding into ao framework and a z system. This time each carbon has two out-ofplane 2p orbitals (see Fig. 6.12 on p. 87) which overlap in two pairs to give two mz bonding MOs and two z anti-bonding MOs. Occupation of all of the o and x bonding MOs accounts for all 10 valence electrons.

6.4

Simple organic molecules

91

o framework m™ system on o framework Fig. 6.17 The bonding in ethyne (acetylene) is similar to that in ethene except that the carbons are now sp hybridized and there are two sets of x interactions.

Carbonyl compounds The simplest carbonyl compound is methanal (formaldehyde), CH20, shown in

Fig. 6.18. The molecule is flat, with bond angles at the carbon of approximately

120°, so the natural choice of hybridization for this atom is sp”. For the oxygen,

the choice is less clear; we know that there is a double bond between the C and the O, so we need to have at least one unhybridized 2p orbital on the oxygen which we can use to form a z bond. So the hybridization needs to be sp? or sp;

for the moment we will choose sp”.

The o framework is simple to describe.

One of the carbon sp? hybrids

overlaps with a hydrogen Is to give a o bonding and anti-bonding MO; two electrons are placed in the bonding MO forming the C-H o bond. The other C-H bond is formed in the same way. The third carbon sp” hybrid overlaps with one of the oxygen sp? hybrids to give a bonding and an anti-bonding o

MO; two electrons occupy the bonding MO to form the C-O o bond.

As the oxygen AOs are lower in energy than those on carbon, the HAOs on oxygen will also be lower in energy than those on carbon. Therefore the major

contributor to the o bonding MO will be the oxygen based orbital; we therefore expect the o bond to be polarized towards the oxygen. The remaining two sp”

hybrids on oxygen are not needed for bonding; they are each occupied by two electrons and so form two lone pairs. H

\o —

/

methanal

(formaldehyde)

H H

eis H

\ C—O.

=s"

sp’-sp*

° framework and lone pairs

@ @ "OO

Hing ——9

m™ system on o framework

Fig. 6.18 Methanal (formaldehyde) has a carbonyl group, that is a C-O double bond. One description of the bonding involves sp* hybridization of both the carbon and oxygen. One of the hybrids on oxygen forms ao bond to the carbon, and the other two are occupied by lone pairs.

Electrons in larger molecules

92

(a)

5

(b) ;

“SO

Hino

O

The z system is essentially the same as in ethene, with the out-of-plane 2p orbitals from oxygen and carbon overlapping to give a m bonding and a

Heine

O

m anti-bonding MO; two electrons occupy the bonding MO, forming the z bond between the carbon and the oxygen. The difference between the 2 bonds in ethene and methanal is that whereas in ethene the two AOs have the same energy, in methanal the oxygen 2p AO is lower in energy than that from carbon.

Fig. 6.19 Cartoons of (a) the

bonding

and (b) the 7 anti-bonding MOs

ina

carbonyl group. The AO on oxygen is lower in energy than that on carbon, and

so the oxygen AO is the major contributor to the bonding MO; for the anti-bonding MO, it is the carbon AO which is the major contributor.

As a result, the oxygen AO is the major contributor to the bonding MO and the resulting 2 bond (like the o bond) % pdlarized towards oxygen. The major contributor to the 2 anti-bonding MO is the carbon, and we will see later on that this is crucial in explaining a great deal of the chemistry of the carbony]

group. Cartoons of these MOs are shown in Fig. 6.19. We should check that all the electrons are accounted for: methanal has 12 valence electrons (two from the hydrogens, four from carbon and six from

=

oxygen). In our description there are three pairs in o bonding MOs, one pair in a x bonding MO and two lone pairs in sp? hybrids on the oxygen; all the

a

C=

ethanal

(acetaldehyde)

H3C Fig. 6.20 The structure of ethanal (acetaldehyde).

electrons are therefore accounted for. The description of the bonding in ethanal (acetaldehyde, Fig. 6.20), CH3CHO, is trivially different from methanal. The methyl carbon is sp? hybridized and uses these HAOs to form the o bonds to the carbonyl! carbon and

the three hydrogens. The description of the bonding in the carbonyl] group is the same as before. We could have chosen the carbonyl oxygen to be sp hybridized, in which case one of the lone pairs will occupy an sp HAO and one will occupy the 2p oxygen AO which is at right angles to the one forming the 2 bond. It makes little practical difference which hybridization state we choose for oxygen as the key features of the bonding in the carbonyl group are not really affected by this choice.

The simplest ester is methyl methanoate (methyl formate), shown in Fig. 6.21. As in methanal the carbonyl carbon and the carbony! oxygen are

sp? hybridized, leading to the same description of the C-O double bond. The C-O-C bond angle at the ester oxygen is 127 ° so sp? hybridization is probably the most appropriate choice for this atom. The methyl carbon is sp? hybridized,

as before. The o framework therefore consists of the C—O bond in the carbonyl! group, the C-H bond to the carbonyl! carbon and the following additional interactions: 7

oe \

Oo

i

C=O

Non ~

H

sp-sph— Sp—

sp?-sp?

~~.

op.

H

methyl methanoate (methyl! formate)

sp*-sp*

\ ( 7

\ Ny

ay

°

; sp*-is

H

Fig. 6.21 Description of the bonding in methyl methanoate (methyl formate); only the o framework and the lone pairs are shown, the x system is the same as in methanal (Fig. 6.18 on p. 91). The ester oxygen is sp hybridized, so one of the lone pairs is in the 2p orbital which points out of the plane in which the hybrids lie.

6.5

93

Reconciling the delocalized and hybrid atomic orbital approaches

three C—H bonds in the methyl group, each formed by the overlap of an sp? hybrid and a hydrogen 1s; a bond between the methyl carbon and the ester oxygen formed by the overlap of a carbon sp? and an oxygen sp? hybrid; and a bond

between the carbonyl carbon and the ester oxygen, formed from sp* hybrids on each.

The remaining sp* hybrid and the unhybridized 2p AO on the ester

oxygen are occupied by lone pairs. Figure 6.21 summarizes the description. The description of amides, such as methanamide (Fig. 6.22), is a little more

complex as it turns out that the lone pair on the nitrogen interacts with the carbonyl z system. We will discuss how this comes about and the consequences it has for both the structure and reactions of amides later on in Section

p. 160.

\o —

10.2 on

/

methanamide (formamide)

HoN Fig. 6.22 The structure of methanamide

Nitriles Nitriles, such as ethanenitrile (acetonitrile), CH3CN, shown in Fig. 6.23, have a

triple bond between carbon and nitrogen; as with ethyne (p. 90) both the carbon

and the nitrogen are sp hybridized. The two hybrids which point towards one another along the C—N axis overlap to form o bonding and anti-bonding MOs; two electrons occupy the bonding MO to form the C-N o bond. The two pairs of out-of-plane 2p orbitals overlap to form two z bonding and two z §anti-

bonding MOs. Together, occupation of the o and the two m bonding MOs forms the triple bond.

The remaining sp hybrid on nitrogen is occupied by two electrons forming

a lone pair; the remaining sp hybrid on carbon is involved in forming a o bond to the methyl carbon. H3C—-C==N _

SP*SP >

ethanenitrile

HgC @@

H3C 7-C——N:i~—sp

OO

soso

o framework

H3C 99 m system on o framework

Fig. 6.23 The C-N o bond in ethanenitrile is formed using sp hybrids on carbon and nitrogen, just as in ethyne (Fig. 6.17 on p. 91); the second sp hybrid on the nitrogen is occupied by a lone pair of electrons. The out-of-plane 2p orbitals form the two x bonds.

6.5

H

Reconciling the delocalized and hybrid atomic orbital approaches

The MO and HAO approaches take a very different view of the bonding in a molecule.

Whereas the MO

picture combines AOs from several atoms, the

HAO picture is strictly a localized one in which bonding is between pairs of atoms; electrons not involved in bonding (lone pairs) are assigned to orbitals

which are localized on a single atom. The question is, do the two approaches give us the same picture of the bonding in a molecule?

(formamide).

Electrons in larger molecules

MO3

view

MO4 view

A

MO4 view B

MO3 view B

Fig. 6.24 Computer

calculated

surface

plots of the occupied

energy, MO2 the next lowest, and so on for MO3

A

and MO4;

MOs

of water.

MO1

is the lowest

this last orbital is the HOMO.

in

All four

orbitals are shown in a view looking down onto the plane of the molecule (view A); a side view of MO3 and MO4

is also shown in view B.

We will explore this question by considering the case of water whose localized bonding description was given on p. 85. In this description the occupied

orbitals are: (1) a

0 bonding MO between the oxygen and one of the hydro-

gens; (2) an identical MO between the oxygen and the other hydrogen; (3) two sp? type orbitals on oxygen, neither of which is involved in bonding.

A computer calculation gives the MOs shown in Fig. 6.24; at first sight these do not appear to have much connection with the localized picture, but on closer inspection it turns out that there are similarities. Consider first the two lowest energy MOs, MOI and MO2. If we form the combination (MOI + MO2) there will be reinforcement on the right-hand side,

where both orbitals are positive, but on the left-hand side the negative part of MO2 will cancel with the positive MO1; the process is shown in cartoon form in Fig. 6.25. The result will be an orbital which is mainly between the oxygen and the right-hand hydrogen; this is the localized orbital between these two atoms. In a similar way if we form the combination (MO1l — MO2) we end up with an orbital which is mainly between the oxygen and the left-hand hydrogen. So, MOI and MO2 can be thought of as representing between them

6.6

95

Orbital energies: identifying the HOMO and LUMO

the two localized o bonds between the oxygen and the two hydrogens.

This picture, of-plane MO as oxygen.

leaves the other two orbitals MO3 and MO4 which, in the localized ought to correspond to our two lone pairs. MO3 is essentially an out2p orbital which is clearly non-bonding. However, MO4 is a bonding it has some electron density shared between the hydrogens and the Clearly, then, MO3 and MO4 do not correspond simply to the two sp

hybrids from the HAO description. In the hybridization approach we made the four sp* hybrids equivalent, SO it is inevitable that when we use these HAOs

to describe the bonding in

water the two orbitals which are occupied by the lone pairs will have the same shape and energy. The MO description imposes no such restrictions and so we should not be surprised to find that the orbitals which are occupied by the lone pairs are not the same. Experiments confirm that this prediction from the MO calculation is indeed correct. The computer generated MOs

the electronic hardly expect and based on between pairs

are certainly a more precise description of

structure of water than is our simple HAO approach. We could it to be otherwise as the HAO approach is purely qualitative simple approximations such as only permitting the interaction of orbitals. Nevertheless the HAO approach does capture the

essence of the bonding in water, namely that there are o bonds between the oxygen and the hydrogens, together with extra electron density on the oxygen.

If we want to think about the shape of the water molecule or the way in which it reacts, the HAO picture is a perfectly good starting point.

In summary, although we recognize the deficiencies of the HAO approach,

it does allow us to make a reasonable start at describing how a molecule is

bonded together, and the form of the orbitals involved, without having to resort to computer calculations. A further advantage of the HAO approach is that it

clearly associates MOs with particular bonds — an idea which fits in well with

the way we think about reactions. When it comes to describing the bonding in larger molecules we will find that a useful approach is to use HAOs to describe the o-framework and then

use the fully delocalized MO approach to describe the rest of the bonding. Typically this means using the MO approach to describe the 7-system. Often the o-framework is not involved in reactions, so it does not matter too much if our description of the framework is approximate. The more precise MO approach is reserved for dealing with the part of the molecule which is actually involved in the reaction. We will use this approach extensively in Chapters 10 and 11.

6.6

Orbital energies: identifying the HOMO

and LUMO

When it comes to chemical reactions it is very important to identify the highest occupied MO (the HOMO) and the lowest unoccupied MO (the LUMO). This is because, as we shall see in the next chapter, these orbitals are the ones which are most directly involved in reactions. Of course, we can always use a com-

puter program to compute the MOs and so identify the HOMO and the LUMO, but in many cases it is not really necessary to go to this level of sophistication.

MO1

M02

Fig. 6.25 Cartoons showing the way in which combinations of MO1 and MO2 from water (shown in Fig. 6.24) give rise to localized o bonding orbitals. The combination MO1 + MO2 results in cancellation on the left-hand side and so gives an orbital which is mostly between the oxygen and the right-hand hydrogen. Similarly, the combination MO1 — MO2 gives an orbital which is mostly between the oxygen and the left-hand hydrogen.

96

Electrons in larger molecules

For our purposes, it will be sufficient to use the HAO approach to draw up a picture of the bonding. As we have seen in this chapter, for simple molecules

this approach allows us to identify electron pairs as being involved in 2c-2e bonds (in o or x bonding MOs) or localized on atoms as lone pairs. All we o* anti-bonding MOs

iW THE

energy ————{>

then need to do is to have a method of ordering these orbitals in energy so that

n* anti-bonding MOs non-bonding orbitals

nm bonding MOs

6 bonding MOs

Fig. 6.26 The approximate ordering of orbital energies found in molecules;

anti-bonding MOs are indicated by a superscript *.

we can determine the HOMO and LUMO.

Typically the ordering of energies is that shown in Fig. 6.26. The o bonding MOs come lowest, followed by 7 boftding MOs; as we commented on above, the sideways-on overlap which leads to MOs is not generally as effective as the head-on overlap which leads to a MOs.

Not surprisingly, next after the bonding orbitals come bitals, which can be AOs, HAOs or, as we shall see, MOs. are the anti-bonding MOs (indicated by a superscript *). that the o bonding MO lies below the z bonding MO, the MO.

the non-bonding orFinally, higher still For the same reason o” lies above the z*

This order of energies is not immutable, but it is a good starting point. So, for example, we can easily identify the HOMO in methanal and ethanal as a lone pair on the oxygen and the LUMO as the z* anti-bonding MO between the carbon and the oxygen.

7

Reactions

In Chapter 6 we looked at the molecular orbitals in some simple compounds.

We now want to see how these are involved in chemical reactions. The energies of the orbitals help us to understand why the reaction occurs and the shapes are crucial in understanding how the reaction takes place. As a model, we shall first consider the hypothetical reaction between a single proton, H*, and a hydride ion, H~, to produce H:

Ht +H” —> Hp.

7.1.

The formation of Hz from H* and H—

It might be tempting to say that this reaction occurs because the reactants are

oppositely charged; however there is more to it than this. The reaction does not lead Fig. 7.1 between opposite

to an ion pair held together by electrostatic (a), but to the formation of a molecule where the two nuclei, as shown in (b). It is true that charges, the ions are attracted to one another

attraction, as shown in the electrons are shared to start with, due to their but as the separation be-

tween them decreases the electrons are redistributed. Initially both electrons are associated with one nucleus, but in the product they are located in a molecular orbital and shared between the two nuclei. This redistribution is shown in Fig. 7.2 which compares the electron density of the separate ions and the

product, H2.

H-

He

H° + H°——» H—-H Fig. 7.1 The reaction between H~ and H* does not give an ion pair, as shown in

(a), but a molecule of Hz, as shown in

(b).

H5

Fig. 7.2 Contour maps showing the electron density associated with (a) the H~ ion and a separate

proton (H+), and (b) with the Hz molecule.

The sharing of the electrons has led to a product lower in energy than the starting materials — it is an exothermic process. Even though the entropy of the system must have decreased as the two ions combined to form one molecule,

the entropy of the Universe has increased due to the heat given out to the surroundings during this exothermic process. Chemists illustrate this redistribution of electrons by using curly arrows,

Fig. 7.3 shows how we can represent the reaction between Ht and H™ using this approach. A curly arrow represents the movement of a pair of electrons.

re

Ho ——»

H—H

Fig. 7.3 A curly arrow mechanism for the reaction between a hydride ion and a proton.

Reactions

98

The arrow starts where the electrons are in the reactant (here in the H™

ion)

and shows where this pair of electrons ends up in the product (in this case in

between the two nuclei in the new bond). This curly arrow representation of the reaction between H* and H™ is prob-

ably not a realistic description of what actually happens. Rather than the two electrons being shared, what probably happens in this case is that one electron is transferred from H~ to H+ to give two H atoms which then come together a

to form H2.

>

Nonetheless, hypothetical though the reaction is, it is a good starting point

for understanding reaction mechanisms.

In the next section we will use this

approach to discuss a real reaction in which a bond is formed by the sharing of

electrons.

7.2

Formation of lithium borohydride

Lithium hydride, LiH, and borane, BH3,

LiBHg:

LiH + BH3 —

react to form lithium borohydride,

LiBHg.

This reaction occurs very readily at room temperature when borane (which

actually exists as a dimer, B2He — see Fig. 6.4 on p. 82) is mixed with the lithium hydride in ethoxyethane (diethyl ether) as a solvent. In this reaction there is a decrease in the entropy of the system since two

molecules go to one. Just as in the case of Ht + H™ the reaction is exothermic so there is an increase in the entropy of the surroundings which, it turns out, more than compensates for the decrease in the entropy of the system. The reason why the reaction is exothermic is because the energy of the electrons in the product is lower than in the reactants. We need to look at the molecular orbitals in the reactants and products to understand why this is so. The left-hand column of Fig. 7.4 shows the MOs of LiH, together with

their approximate energies, which have been calculated using a computer program. We have already drawn a qualitative MO diagram for this molecule, Fig. 5.23 on p. 78. In doing this we ignored the 1s orbital on lithium, arguing that it was too low in energy to interact with the hydrogen Is. In Fig. 7.4 MO-

LH1 is essentially this unchanged lithium 1s orbital; MO-LH2 is the bonding MO formed by overlap of the lithium 2s with the hydrogen 1s (labelled lo in

Fig. 5.23, which is also’ shown

as a contour plot in Fig. 5.24 on p. 78). The

unoccupied anti-bonding MO is not shown. In Chapter 6 we used sp* hybrids to draw up an approximate MO diagram for BH3 (Fig. 6.11 on p. 86); as for LiH, we ignored the 1s orbital on B. We

identified three bonding MOs and one non-bonding MO, the out-of-plane 2p orbital. The right-hand column of Fig. 7.4 shows computer calculated MOs for BH3. As we described in Section 6.5 (p. 93) the MOs calculated in this way are delocalized and so do not compare directly with the simpler localized HAO description. However, we can clearly identify three bonding MOs, MO-B2, MO-B3 and MO-B4, together with the non-bonding MO, MO-BS, which is the

LUMO. MO-B1 is essentially the boron |s orbital which is not involved in the bonding.

7.2

99

Formation of lithium borohydride Lithium hydride MOs

or

Lithium borohydride MOs

Borane MOs

a deaenans

ers

a-

MO-LH2 (LiH HOMO)

—_—

—

x

rf

MO-P6

-8 eV

f

MO-B5 (BH, LUMO)

(LiBH, HOMO) -11 eV

+2 eV if occupied

ees MO-P5 -11 eV

©

~12 eV him e-

mice N

ze

\

SO

8

Boxe;

Li

«-~

~

MO-P3

-19 eV

“e- > oe eae

ae

a

HO

f

if

H

a

MO-B2 -19 eV

O MO-P2 -67 eV

Pee

¥

SH/B

eae

fe

MO-P1

-203 ev

Fig. 7.4 The left-hand column shows the occupied MOs of LiH. The energies are given in eV; a negative energy means a more tightly held electron. The right-hand column shows the occupied and the LUMO for BH3. The middle column shows the occupied MOs for the product, LiBH4. The important orbitals for each molecule are shown at the very top. In the LiBH, structure the dashed are used to illustrate the arrangement of the atoms rather than to imply the existence of bonds.

more MOs most lines

Just as we can think of a molecular orbital as being formed from two atomic orbitals, we can think of the MOs in the products as arising from the interactions between the MOs in the starting materials. The middle column of Fig. 7.4 shows the occupied molecular orbitals in the product, LiBH4.

Reactions

100 Unoccupied MO (not shown)

@

HOMO

Hi

HP,

++

+

of LiH

(MO-LH2)

OC)

Li

D

©

LUMO

of BH

)

(MO-BS)

H'!tiuiB—H

HOMO

LiBH,

in

(MO-P6)

Fig. 7.5 Schematic energy level diagram for the interaction between the HOMO of LiH and the LUMO of

BH3.

The lowest energy MO, MO-P1, is essentially the unaffected boron 1s AO which correlates with MO-B1

from BH3.

lithium which correlates with MO-LHI

Likewise, MO-P2

is the 1s AO on

on LiH. The boron Is orbital is much

lower in energy than the lithium because boron has a larger effective nuclear charge. These 1s orbitals remain virtually unchanged in the product. Comparing the MOs in borane and the product we see that MO-B2, MO-B3

and MO-B4 have similar forms and energies to MO-P3, MO-P4 and MO-P5, respectively. Thus occupation of these MOs makes little contribution to the

energy change of the reaction. In contrast, the HOMO of LiH (MO-LH2) and the LUMO of BH3 (MO-B5) are changed significantly on forming the product. MO-LH2 has no compara-

ble orbital in the product and even though the HOMO in the product (MO-P6) looks rather like the LUMO

in borane (MO-BS) their energies are very differ-

ent, with MO-P6 being much lower.

In summary, we can attribute the lowering in energy when LiBHg is formed to the two electrons from the HOMO of LiH (MO-LH2) moving into the lower

energy HOMO

of LiBH4 (MO-P6).

from the interaction of the HOMO

schematically in Fig. 7.5.

LUMO

This orbital can be thought of as arising

of LiH with the LUMO of BHs3, as is shown

As we will see in the next section, such HOMO-

interactions are often of particular importance in reactions.

HOMO-LUMO

interactions

Usually, it is the interaction between filled orbitals of one reactant with va-

cant orbitals of the other which leads to a favourable lowering of the energy. The interactions between two vacant orbitals is of no consequence as they are unoccupied and so there is no change in the energy of the system. The interac-

tions between two filled orbitals have little net effect on the total energy of the system since the decrease in energy from the newly formed in-phase combination is essentially cancelled out by the increase in energy of the corresponding

out-of-phase combination. Only the interaction between a filled orbital and an empty orbital leads to a net lowering of the energy of the electrons, as shown

in Fig. 7.6.

7.2

Formation of lithium borohydride

101

a (b)

(a)

Fig. 7.6 The interaction of two empty orbitals as shown in (a) does not lead to a lowering since there are no electrons whose energy is being lowered. In the interaction between orbitals, shown in (b), two electrons are lowered in energy but this is cancelled out by the two which are raised in energy. Only in (c), the interaction between an empty and a filled orbital, net lowering in the energy since the orbital which is raised in energy is unoccupied.

in energy two filled electrons is there a

Of course there are many filled and vacant orbitals which can interact — the

question is which interaction is the most important? Recall from the discussion on p. 67 that the strongest interaction is between orbitals of similar energies, so the best candidates for a favourable interaction will be an unoccupied MO and an occupied MO which are close in energy.

If the energies of the MOs of the two reactants are broadly similar, then we can expect the best energy match to be between the LUMO of one with

the HOMO

of the other, as shown in Fig. 7.7. There is no guarantee that this

HOMO-LUMO interaction will be the most favourable, but it turns out that it is often so. When two species meet, two HOMO-LUMO interactions are possible; there is an interaction between the HOMO of reactant A with the LUMO from reactant B and also between the HOMO from B with the LUMO from A. The very best interaction is usually between the occupied MO which has the highest energy of either reactant with the LUMO

smallest energy difference.

tween the HOMO

from B

The interaction (shown with the dotted line) be-

separation in energy is greater.

of A

is less significant because the

Frequently we will find that we can understand the outcome of a reaction

between two molecules by first identifying which molecule has the very highest occupied MO and then considering the interaction between this and the LUMO

of the second molecule. In the reaction between LiH and BHs3, the very highest occupied MO is the HOMO of the LiH (MO-LH2). This is considerably higher

in energy than the HOMO between the HOMO

of the BH3 (MO-B4) so the main interaction is

from the LiH and the LUMO

from the BH3, MO-B5.

.

a

from

since these two MOs are separated by the

of B and the LUMO

s

+

from the other reactant. In Fig. 7.7,

the best interaction (shown with the wavy line) is between the HOMO reactant A with the LUMO

Hao

HOMO

MOs for

te

HOMO

MOs for reactant B

reactant A

Fig. 7.7 The strongest interactions are between the HOMO of one molecule and the LUMO of another. For the set of MOs shown here, the best interaction, shown

by the wavy line, is between the HOMO of reactant A and the LUMO

of reactant

B. Since the HOMO of A is particularly

high in energy, the energy gap between

this and the LUMO in B is particularly smail.

Orbitals and curly arrows Just as we did for the Ht + H™ reaction, we can use curly arrows to illustrate,

in a concise way, what is going on in the reaction between LiH and BH3. From studying the orbitals we see that a pair of electrons from the o-bonding MO of

LiH (the HOMO - MO-LH2) end up in an orbital of LiBHy4 which contributes to the formation of a new B-H bond. Figure 7.8 illustrates this process using

a curly arrow. The arrow starts where the electrons come from — the bond between the Li and H — and finishes where the electrons end up, in a new bond between the H and the B. It tells us that the electrons that were bonding the Li

H |

ui-Lny

H

rie

Li

H

©

H | 9 Bi,

H~ ¥

H

Fig. 7.8 The curly arrow mechanism for the reaction between borane and lithium hydride.

Reactions

102

and H are now helping to bond the H to the B. Since the lithium has effectively lost The one now

its share of electrons from the Li-H bond, it ends up with a positive charge. BH3 molecule initially had no charge; in forming the product it has gained extra proton and the two electrons that were in the Li-H bond. It therefore has a negative charge. In LiBHg, the lithium is mainly attracted to the rest of the molecule elec-

trostatically. Its MOs shown in Fig. 7.4 show little evidence of electrons being shared between the lithium and the rest of the molecule and a calculation confirms that the lithium does indeed bear a substantial positive charge with the corresponding negative charge being spread out over the boron and hydrogen atoms. The HOMO

in lithium borohydride is still fairly high in energy. In the next

section we shall see how the interaction between this and a suitable LUMO

allows us to understand the use of LiBHy as a reducing agent.

7.3

Nucleophilic addition to carbonyl

Nucleophilic addition to a carbonyl group is one of the most important reactions in organic chemistry. In this reaction a nucleophile attacks the carbonyl

group, forming a new bond to the carbon and simultaneously breaking the C-O m bond; Fig. 7.9 shows the reaction of a general nucleophile, Nu.

Hydroxide,

cyanide (CN7) and alkyllithium reagents (R-Li) are all examples of nucleophiles which will attack carbonyl groups in this way.

fe) R

R ‘

Nu

o Lun,

v'R' R

Fig. 7.9 The reaction between a carbonyl group and a nucleophile, Nu~. In this case the nucleophile is negatively charged, but this is not a requirement — neutral species can also act as nucleophiles.

This simultaneous breaking of the bond is the added complication we now Ho

4

H@

y

O

~H

—-

of

H~

6,

¥,H

Fig. 7.10 The reaction between methanal and hydride: this is an example of nucleophilic addition.

need to consider. In order to look at the changes in the MOs we will consider

the simplest possible example of this reaction which is the attack of a hydride ion on methanal (formaldehyde) shown in Fig. 7.10.

HOMO-LUMO interactions for the carbonyl and nucleophile The two reactants are initially attracted towards each other since the carbonyl carbon has a partial positive charge and the hydride ion is negatively charged. However, the two reactants do not just remain attracted towards each other electrostatically; bonds are formed and broken. In other words, electrons are

redistributed.

The reaction starts with a negative charge on hydrogen and ends with the

charge on oxygen.

Since oxygen has a greater effective nuclear charge than

hydrogen, having the increased electron density on oxygen is favourable and so contributes to the lowering of the energy of the product.

We can see how this redistribution of charge takes place by looking at the HOMO-LUMO interactions. The highest occupied MO in the whole system is from the H™ ion. The vacant orbital closest to this in energy is the LUMO

7.3.

Nucleophilic addition to carbonyl

methanal LUMO

Ata

Pt

scans “SEES

Fig. 7.11 The in-phase interaction between the methanal x* and the hydride HOMO. In diagram (a) two orbitals are shown: the occupied hydride MO and the unoccupied methanal 7*. Diagram (b) shows the orbital arising from the in-phase overlap of the HOMO and LUMO at an intermediate stage in the reaction. Electron density is building up on the oxygen at the expense of the hydride. The corresponding MO in the product is shown in diagram (c). This is essentially a p orbital on the oxygen, i.e, a lone pair; there is little electron density on the hydrogen when compared to (a).

of the methanal, the 7*. Figure 7.11 (a) shows the initial interaction of these two orbitals, and (b) shows the orbitals at an intermediate stage in the reaction.

The MO

formed from the in-phase interaction between the hydride HOMO

and methanal LUMO

shows that electron density is being transferred from the

hydride onto the oxygen. This is even more apparent in the product MOs shown in Fig. 7.11 (c) where there is much more electron density now on the oxygen and relatively little on the hydrogen. The hydride HOMO and the methanal LUMO also combine out-of-phase

to give an anti-bonding orbital higher in energy than the methanal LUMO; this

anti-bonding orbital is not occupied.

The hydride HOMO is closest in energy to the CO 2* MO and so has the strongest interaction with this orbital. However, it also has an interaction with

the CO x MO, and it turns out that it is this interaction which explains how the CO x bond is broken. Fig. 7.12 shows the in-phase interaction between these two orbitals.

At an intermediate stage, shown in (b), we see the interaction between the carbon and oxygen begins to weaken. In the product, shown in (c), there is

methanal mt MO

Fig. 7.12 The interaction between the methanal x MO and the hydride HOMO. Diagram (a) shows the two orbitals as the two reactants approach each other. Diagram (b) shows the orbital arising from the

in-phase overlap of these the C and O is beginning In the corresponding MO and O, only between the

two orbitals at an intermediate stage in the reaction. The bonding between to weaken while that between the C and the approaching H is strengthening. in the product, shown in (c), there is effectively no bonding between the C C and H.

103

104

Reactions electron density between the C and the H but rather little between the C and O. Just as we expected, a bond is formed between the C and the H and the C-O x

bond is broken. , The interaction of these three orbitals — the hydride HOMO, the z and the m* — gives rise to three new MOs in the product (recall that the number of orbitals is conserved); Fig. 7.13 shows a sketch of the relative energies of the MOs. The exact energies of these MOs can only be obtained from a computer calculation, but we can see from the diagram that the total energy of the electrons has been reduced. “empty.

MO

*

CO x*

COnr C-H bond methanal MOs

product MOs

hydride AO

Fig. 7.13 Key orbital interactions between the hydride HOMO and carbonyl 7 and 2* MOs.

Curly arrows

Figure 7.14 uses curly arrows to show the important features of the changes that take place during the reaction between hydride and methanal. H

OF

\

we

H

CN,,

—_—_—_—

(o)

O~

7 4

Cony H

Fig. 7.14 The curly arrow mechanism for the reaction of methanal with hydride.

The arrows show that the hydride ion attacks the carbonyl carbon and that a new bond forms between the carbon and the hydrogen. They also show that

the z bond breaks and electron density ends up on the oxygen.

The arrows imply that it is the pair of electrons from the 2 bond which end up forming the negative charge on the oxygen. However, in Fig. 7.11 it

is implied that the pair of electrons from the hydride orbital end up on the oxygen. This apparent contradiction can be resolved by noting two things. Firstly, the arrows in Fig. 7.14 relate to a structure in which the electrons are localized in 2c-2e bonds or as lone pairs (charges). In contrast, the MOs shown

in Fig. 7.11 are delocalized over all three atoms, and so there is not a one-to-one correspondence between the two pictures. Secondly, it is not really possible to say from which reactant MO a pair of electrons in a product comes from. For example, looking at Fig. 7.13, how can we decide which pair of electrons ends up in the middle energy MO when ail of the reactant orbitals contribute to this?

7.3

Nucleophilic addition to carbonyl

105

So there really is no contradiction between the MO picture and the curly

arrows. They are just different ways of representing the same thing — the curly

arrows relate to a strictly localized view of bonding whereas the MOs relate to a delocalized approach. The important point is that the curly arrows give the same result as the MO approach: in this case a new bond is formed between the carbon and the attacking hydride nucleophile, the C-O z bond is broken, and a negative charge ends up on the oxygen.

The geometry of attack For the hydride to interact with the 7 and x* orbitals, it must approach from the right direction. If it were to approach the carbonyl in the same plane as the molecule, there will be no net interaction since the constructive and destruc-

tive contributions will cancel one another out. This is shown schematically in

Fig. 7.15 (a).

(a)

(c)

constructive

~

ax

Oa

a

destructive

1* of carbonyl

hydride MO

Fig. 7.15 The angle which the attacking nucleophile approaches from is important. approaches

In (a) the hydride

in the same plane as the carbonyl — there are equal amounts of constructive and destruc-

tive overlap leading to no net interaction. Similarly there is no net overlap in (b) where the hydride approaches from directly over the carbonyl group. The best angle of attack is shown in (c).

Similarly, if the hydride were to approach from above and directly in between the carbon and oxygen, as shown in (b), there would be no net overlap. Detailed calculations and experimental evidence suggests the best angle of ap-

proach is approximately 107° from the carbonyl, as shown in Figs. 7.15 (c) and 7.16. This maximizes the degree of constructive overlap and also minimizes the repulsion between the filled 2 orbital and the incoming nucleophile. Borohydride reduction of a ketone We will finish this section by describing a reaction which can be carried out in the laboratory and which effectively results in the addition of H~ to a carbonyl

group. Rather than using H™ directly, we use the reagent sodium borohydride, NaBHg4, which reacts with aldehydes and ketones to give the corresponding alcohol. The reaction is, of course, a reduction as it involves the addition of hydrogen.

The MOs for NaBH, are very similar to those of LiBH4 which are depicted in Fig. 7.4 on p. 99. The highest energy occupied MO (MO-P6) is one which is involved in the bonding between the boron and the hydrogens. When boro-

hydride acts as a nucleophile, it will be the electrons in this HOMO which are primarily involved.

—

ep

Fig. 7.16 The optimum angle of attack by a nucleophile on a carbonyl group.

106

Reactions

“VI H H3C

CHs

OO

oH

‘ows

47

ViCHs 3

Fig. 7.17 The reaction between orohydride, BH, , and propanone.

Having identified the HOMO of the system, we need to identify the LUMO of the other reagent. For a ketone such as propanone (acetone) the LUMO is once again the z*. As before, the interaction with the HOMO results in the z

bond being broken and the electron pair moving to the oxygen; a curly arrow mechanism for this is shown in Fig. 7.17.

Figure 7.17 shows the electrons from the B—-H bond attacking the carbon of the carbonyl. This results in the B—H bond breaking and a new C—H bond |

SNH

Cc, Vv‘H

@

_

tT

HH

OH |

Cc, v'H

aN

Hy

Fig. 7.18 A curly arrow mechanism for the protonation of the anion formed from

the reduction of methanal.

being formed. At the same time, the C—O z bond is broken, leaving a negative charge on the oxygen just as before.

The final step is to add acid which reacts with the -O~ to give an alcohol,

as shown in Fig. 7.18.

The HOMO

of the anion is certainly the lone pair of

electrons on the oxygen and the LUMO form a new bond to H*

Section 7.1 on p. 97.

7.4

is the 1s on H+.

These interact to

in much the same way as the reaction discussed in

Nucleophilic attack on C=C

A carbon-carbon double bond has the same 7 orbitals as a carbon-oxygen double bond so we might expect nucleophiles to attack C=C in the same way

they attack C=O. However, this is not the case — nucleophiles do nor usually attack alkenes. In fact, alkenes often act as nucleophiles themselves, preferring

to donate electrons rather than accept them. We can understand these differences by considering the nature of the C=C bond and the orbitals involved. Firstly, unlike in the carbonyl, the C=C bond

does not have a dipole moment so there is no electrostatic attraction to bring the alkene and nucleophile together. The next main point to consider is the energies of the orbitals involved; these are shown in Fig. 7.19. The z* MO of the C=C bond is higher in energy than the 2r* of the C=O

Fig. 7.19 Due to the energy differences between the atomic orbitals of carbon and oxygen, the C=C x and z* MOs are higher in energy than the corresponding orbitals of C=O.

7.5

Nucleophilic substitution

bond.

107

This means that there is a poorer energy match between the C=C

x*

and the HOMO of any attacking nucleophile. As we have seen, the poorer the

energy match, the weaker the interaction will be.

The final point is that if a nucleophile did attack a C=C, a new bond will

form between the carbon and the nucleophile and the carbon-carbon double

bond will break leaving the charge on a carbon, as shown in Fig. 7.20. This is not as favourable as the attack on the carbony! where the negative charge ends up on the oxygen atom, the reason being that the oxygen orbitals are lower in

energy — put another way the charge is best located on an electronegative atom.

Taking these factors together provides a rationale for why nucleophilic attack on C=C does not occur whereas attack on C=O occurs readily. Nu°

Nu

~oC=Cm

U

\

S)

CC

aN

Fig. 7.20 If a nucleophile did attack a C=C » bond, a negative charge would form on the other carbon atom. Unlike having a negative charge on oxygen, this is not favourable.

7.5

Nucleophilic substitution

We are now going to look at a reaction in which the nucleophile donates elec-

trons not into an empty AO or a z* MO but into a o* MO. This will lead to the breaking of the o bond, so an atom or group will break away from the molecule. The reaction is therefore called nucleophilic substitution as opposed

to the addition reaction we have seen so far. A typical example is where an incoming nucleophile, Nu~, bonds to the

carbon of chloromethane, displacing Cl” in the process:

Nu” + CH3Cl —> CH3Nu4+ Cl". In chloromethane the only unoccupied MOs will be o* MOs, of which there

are two different types: the C-H and the C-Cl a”. The nucleophile HOMO will interact most effectively with whichever of these is lower in energy; as we will

see in the next paragraph, it turns out that this lowest energy MO is the C-Cl o*. The energy of the o* MO will depend on the strength of the interaction

between the two AOs involved, and this depends primarily on the energy separation of these orbitals. As the chlorine AOs are lower in energy than those

of the hydrogen, there will be a better match between the AOs involved in the C-H interaction than in the C-Cl interaction. As a result the o* MO for the C-Cl bond will be lower in energy than the corresponding orbital for CH; this is illustrated in Fig. 7.21. In larger halides such as chloroethane, there are also C-C interactions. However, these C-C interactions also involve well-matched AOs, so again we

expect that the resulting o* MO will be higher in energy than for C-Cl. In fact, of the 0* MOs in such molecules, it will always be the case that the MO associated with a bond to an electronegative element (such as Cl, N or O) will be

108

Reactions

(a)

(b)

Fig. 7.21 Due to the larger difference in energy between the carbon and chlorine AOs than between the carbon and hydrogen AOs, the C-Cl o* will be lower in energy than the C-H o*.

lower in energy than the 0* MOs from C-C or C-H bonds. This is why much

organic chemistry often centres around the functional groups which contain atoms other than carbon and hydrogen, leaving the basic C-C / C-H framework intact. The anti-bonding MOs involving the heteroatoms are inevitably

lower than those in the basic framework and hence more readily involved in

reactions. A contour plot and surface plot of the C-Cl

o* MO

(the LUMO)

from

chloromethane is shown in Fig. 7.22 together with a schematic representation.

1C

y/]

4H

“ig

\

y

Cl

V4

Fig. 7.22 Three representations of the LUMO (the C-Cl o* MO) in chloromethane: a contour plot, a surface plot and a sketch. Note the node between the C and Cl, and the lobe on C which points away from the bond.

The reaction between hydroxide ion and bromomethane We shall look at the reaction between a halogenoalkane, in this case bromomethane and hydroxide ion. This is a simple substitution reaction where

the hydroxide takes the place of the bromide ion:

.

HO™ + CH3Br —> CH30H+ Br’.

Having identified the LUMO as the C-Br o* MO, we need to identify the

HOMO

that this will interact with.

Not surprisingly, this is the orbital occu-

pied by one of the lone pairs on the oxygen of the hydroxide ion. The overall negative charge raises the energy of this orbital further. For simplicity we will assume that the lone pair occupies an sp? orbital on the oxygen — the details are not really important for this discussion.

7.5

Nucleophilic substitution

109

The angle of approach

A 8+ 8

Bromomethane has a dipole moment with the carbon atom slightly positively

charged and the bromine atom slightly negatively charged (Fig. 7.23). The negatively charged hydroxide ion is therefore attracted towards the carbon.

best interaction of the HOMO

of the hydroxide and the LUMO

The

of the bro-

momethane is achieved if the nucleophile attacks the carbon from the opposite

side to the bromine. This attack is shown enema H

in ne 7.24,

LUMO of bromomethane

new o Mo" between C and O

Fig. 7.23 Due to the differences in the electronegativities of carbon and has a dipole

moment with the carbon atom being slightly positive and the bromine atom

\ O@ - @:000 —- @6- 0 aM

HOMO of hydroxide

H oe

bromine, bromomethane

H

e

H! y C—Br

slightly negative.

HOMO of bromide

Fig. 7.24 The hydroxide ion attacks the bromomethane from directly behind the C—Br bond since this maximizes the interaction with the LUMO (the C—Br o*) of the bromomethane.

If the nucleophile were to attack the carbon atom from the side, the orbital

overlap would be poor due to the symmetry mismatch (Fig. 7.25). During the reaction, the HOMO of the hydroxide interacts with the LUMO

of the bromomethane, the C-Br o*. A new o bond forms between the carbon and oxygen at the same time as the old C—Br o bond breaks. Eventually the bromide ion leaves, carrying with it the negative charge. The curly arrow

mechanism for the reaction is shown in Fig. 7.26. 4

See ‘4

Fig. 7.26 A curly arrow the square brackets is a but just an arrangement carbon centre has been

—

|

HO--C--Br| =b HH

HOMO of

H

Of

@:00 dG Cc

ic}

-——»

/

H

HO-—C,,

¥H H

BP

mechanism for the attack of hydroxide ion on bromomethane. The species in transition state (see Section 9.2 on p.133) which is not an isolable compound of atoms through which the system passes during the reaction. Note that the inverted during the reaction.

The inversion of the carbon centre

During the course of the reaction, the carbon centre undergoes an inversion —

it is basically turned inside-out with the molecule passing through an arrange-

ment in which all three hydrogen atoms lie in a plane perpendicular to the C-Br bond. This is similar to the inversion of ammonia described in Fig. 6.13

on p. 87.

For the reaction of bromomethane, there is no way that we could tell that the

carbon atom has undergone an inversion. If, however, instead of three hydrogen atoms, the carbon has three different groups around it, then the inversion can be detected. This was demonstrated very neatly in a variation on the reaction involving radioactive iodide attacking 2-iodooctane as shown in Fig. 7.27.

The non-radioactive starting material 2-iodooctane and the product are not the same even when the radioactive atom is ignored. As can be seen in Fig. 7.28, they are in fact non-superimposable mirror images of each other.

C)

hydroxide So-—

Bri

LUMO of bromomethane

Fig. 7.25 If the hydroxide ion attacked the carbon more from the side, the orbital

overlap is much worse due to the

constructive and destructive interactions with the o* orbital.

Reactions

110

H

I

£4 Hac

———_»

i

| r--c--1 = H3C

CeHi3

io}

| ———>

ae i

Ir-C,,

\/CHs

CeHi3

CeHi3

Fig. 7.27 The inversion at the carbon centre can be detected in this experiment involving the substitution of the iodine atom in 2-iodooctane by a radioagtive iodide ion, denoted with an asterisk.

Compounds which are non-superimposable mirror images are called enan-

H

\

/

wo!

tiomers or optical isomers. The term optical isomers arises from the fact that

whilst (R)-2-iodooctane and (5)-2-iodooctane behave the same chemically, one

H

I*—C,,,

¥°CH3

H3C'4

CeHi3

CeHy3

(S)-iodooctane

(F)-iodooctane

Fig. 7.28 The starting material and product are non-superimposable mirror images of each other (ignoring the different isotopes of iodine). These

isomers are differentiated with the labels Sand A.

isomer will rotate plane-polarized light clockwise, while the other isomer will rotate it anti-clockwise. In the experiment, the rate of substitution in the reaction was followed by monitoring the incorporation of radioactive iodine into the 2-iodooctane; the rate of inversion was followed by measuring the degree to which plane-

polarized light is rotated. The results clearly showed that each time a substitution occurred, the molecule underwent an inversion, which is what we would

predict for this mechanism.

7.6

Nucleophilic attack on acyl chlorides

So far we have described reactions in which the HOMO of the nucleophile interacts with a LUMO which is either a 7* MO (for example, in ketones and aldehydes) or ao* MO (for example, in an alky] halide). What happens if the

molecule which the nucleophile attacks has both 2* and o* MOs available? A simple example is the reaction between hydroxide ion and ethanoyl (acetyl) chloride, whose structure is shown in Fig. 7.29. The reactive carbon

centre has both a double bond to oxygen and a bond to chlorine. With both these electronegative elements withdrawing electrons, the carbon has a partial

positive charge but which orbital will a nucleophile such as hydroxide attack into? The hydroxide could either attack into the 2* of the C=O giving a tetrahedral species as shown in Fig. 7.30 (a) or it could attack into the C-Cl o* to form ethanoic (acetic) acid as shown in Fig. 7.30 (b).

Fig. 7.29 Ethanoy! chloride.

The final product from the reaction of ethanoy] chloride with aqueous hydroxide is in fact the carboxylic acid so it is tempting to conclude that mechanism (b) is correct and that the hydroxide attacks into the C-Cl o* MO.

HO (b)

Hsc~

C

Cl

—_—

LN O

H3C

, HO.

C

is tempting but sadly incorrect! In order to understand what does happen, we

Cl need to consider the orbitals involved.

A computer calculation reveals that the LUMO for ethanoy! chloride is the

20

* MO with the C-Cl o* MO lying somewhat higher in energy. These orbitals

are shown in Fig. 7.31. The initial attack by the hydroxide nucleophile is into the C~O

Fig. 7.30 Two possible routes of attack on ethanoy! chloride.

It

In (a) the hydroxide

attacks into the C—O 2* MO and in (b) it attacks into the C—Cl a* MO.

m1* MO

as shown in Fig. 7.30 (a).

There are two reasons why the

nucleophile prefers to attack this MO rather than the C-Cl o*. Firstly, there is a better energy match between the HOMO of the hydroxide and the C—O z* MO. This is because the C—Cl o* is higher in energy than the C-O x”.

7.6

Nucleophilic attack on acyl chlorides

111

dor

Fig. 7.31

Surface

plots and cartoons of two MOs

from ethanoyl chloride:

Oe

(a) is the LUMO

and (b) is

the next highest energy MO. The LUMO is essentially just the C-O 1* MO and the orbital shown in (b) is essentially the C-Cl o* MO with some minor contributions from the other atoms.

Secondly, it is easier for the nucleophile to approach the 3* MO in the correct orientation. As we saw in Fig. 7.16 on p. 105, the best direction of approach for the nucleophile to attack the 7* MO is from above the plane of the C=O bond. This approach is unhindered in the case of hydroxide attacking

ethanoy] chloride. In contrast, when a nucleophile attacks a o* MO it must approach directly from behind, as shown in Fig. 7.24 on p. 109. In the case of hydroxide attacking ethanoyl chloride this approach is hindered by the methyl group and the oxygen, both of which are in the same plane as the 0* MO. Overall, then, attack on the 7* MO is the preferred route. However, as shown in Fig. 7.30 (a), this leads to what is called a tetrahedral intermediate.

What we now need to work out is how this intermediate reacts further to give what we know to be the product, ethanoic acid, as shown in Fig. 7.32.

3

(er

ovo Cl

%,,,_/ Cc

OH

Hsc” cI

O

---- >

I

C

—™~

+

co)

Cl

Fig. 7.32 The initial reaction between the hydroxide and ethanoyl chloride produces a tetrahedral intermediate. This then goes on to form the final products, ethanoic acid and a chloride ion.

The tetrahedral intermediate has no z bond and therefore no 2* MO either, so the C-Cl o* MO (which has remained almost unchanged after the attack of the hydroxide) is now the LUMO of the system. The lone pair of electrons on the negative oxygen is the HOMO in this molecule and, as we commented before, the negative charge raises the energy of this orbital. The interacting HOMO and LUMO are in this case in the same molecule; these orbitals in-

teract to form some new orbitals in the product as shown in Fig. 7.33.

The

overall process is rather more complex than this figure suggests, as more orbitals are involved. A curly arrow mechanism for the whole reaction is shown in Fig. 7.34.

112

Reactions

©

/

,

~,

6

OH

OH

Fig. 7.33 The HOMO of the intermediate shown in (a) is essentially just a lone pair on the oxygen. This orbital interacts with the LUMO, the C-Cl o* shown in (b), to contribute to the MOs of the products. Diagram (c) shows two MOs in the products: the new C-O bond and the p orbital on the chloride ion.

g)

(“oH

~=Cc—Ccl

7

——

%,,,,-/

H,c”

Cc

OH ~

rotate

—=

cI Oo

oO,

"ny

CH

—

o=—

cl CH

"OH

3

Fig. 7.34 A curly arrow mechanism for the reaction between hydroxide and ethanoyl chloride. The intermediate has been rotated after the initial attack to show more clearly how the final products are formed.

This attack on the C-O x” by a nucleophile to give a tetrahedral intermediate and then the subsequent reformation of the C—O z bond is a common reaction which you will meet many other examples of in later chapters. One

example is the reaction between a carboxylic acid, such as ethanoic acid, and

an alcohol, such as methanol, to give an ester as shown in Fig. 7.35.

H3C~

iC

OH

+

CH3OH

fe) I H3c~

Cc

~O~

CH3z

+

H20

Fig. 7.35 The reversible formation of methyl ethanoate (an ester) and water from ethanoic acid and

methanol.

We can also carry out this reaction in reverse, i.e. by adding water to the ester and allowing the hydrolysis reaction to produce the carboxylic acid and alcohol. In other words, this reaction is reversible.

Exactly why some reactions seem to be able to go in both directions and how chemists can try to alter the conditions to favour either the products or the

reactants is the subject of the next chapter.

8

Equilibrium

In Chapter 2 we saw that whether or not a process will ‘go’ is controlled by the Second Law of Thermodynamics. What this law says is that a process will only be spontaneous — that is, take place on its own without continuous

intervention from us — if it is associated with an increase in the entropy of the

Universe (Section 2.2 on p. 7). We also saw that another and entirely equivalent way of applying the Second Law is to express it in terms of the Gibbs energy

(Section 2.7 on p. 16); using this, a spontaneous process is one Gibbs energy decreases. Using either of these criteria we were able to explain why it will freeze at —5 °C but not at +5 °C, since it is only at the lower that water —> ice is accompanied by an increase in the entropy of or, equivalently, a decrease in the Gibbs energy.

in which the is that water temperature the Universe

Applying the same ideas to chemical reactions is rather more subtle, as we need to explain what determines the position of equilibrium, an idea introduced on p. 5 and illustrated in Fig. 2.1. Some reactions go almost entirely to prod-

ucts so the position of equilibrium lies very much towards the products; others hardly go at all and so the position of equilibrium lies towards the reactants.

Other reactions come to equilibrium with significant amounts of reactants and

products present. Our task in this chapter will be to work out what determines

this position of equilibrium.

8.1

The approach to equilibrium

On p. 6 we discussed the equilibrium between NO2 and N20Oq:

2NO2(g) = N204(g)

>

and pointed out that the reaction could come to the equilibrium position (at which significant amounts of both reactants and products are present) either starting from pure reactants (NO2) or from pure products (N2O4). What this implies is that in going from either pure products or pure reactants to the equilibrium position the Gibbs energy must decrease. In other words, the equilibrium mixture of reactants and products has lower Gibbs energy than either pure

products or pure reactants. Shown in Fig. 8.1 is a plot of the Gibbs energy of the mixture of reactants

and products (here NO2 and N2Og) as a function of the composition. Pure reactants correspond to no reaction having taken place and so appear on the

left; pure products correspond to complete reaction and so appear on the right. From

the graph we see that the Gibbs energy goes to a minimum

at some

point intermediate between pure reactants and pure products; this minimum corresponds to the equilibrium position.

5 | equilibrium

elt

Cc o 2

2 oO

——_—_>

2NO,

composition

NoO,

Fig. 8.1 Plot of the Gibbs energy of the reaction mixture as a function of its composition for the dimerization of NOo. The left-hand side of the graph corresponds to pure reactants and the

right to pure products. The minimum in the Gibbs energy corresponds to the position of equilibrium which can be approached either from pure reactants or pure products.

Equilibrium

114

No matter whether we start with pure products, or pure reactants, or some

mixture of the two, the Gibbs energy falls as we approach equilibrium. For example, in Fig. 8.2 if we start at composition a, moving to a’ is accompa-

55

nied by a decrease in the Gibbs energy. The change from a to a’ is therefore a spontaneous process which moves us towards the position of equilibrium by

equilibrium

5

|

Cc wn

y

2

2

Oa

i

L

increasing the amount of products. Starting at b and moving to b’ is also accompanied by a decrease in the Gibbs*enérgy and so will be spontaneous; as

:

I

a’

b'b

——_——

Fo

composition

5

2

g

ae]

8

5

Fig. 8.2 Starting from point a the Gibbs energy will fall as we move to point a’; such a change will be spontaneous and will take us toward the position of

equilibrium by increasing the amount of products. In contrast, from point b the direction which involves a reduction in

Gibbs energy is towards point b’; for this spontaneous change the amount of products is reduced. Starting from either aor b the direction of spontaneous change is towards the equilibrium position, at which the Gibbs energy is a minimum.

for the change from a to a’, the change from b to b’ also moves us towards the equilibrium position but this time by decreasing the amount of products.

The shape of the graph therefore funnels the composition towards the value with the minimum Gibbs energy, which is the equilibrium position. From this point any change would involve an increase in the Gibbs energy, which is not permitted. So, once at its equilibrium value the composition cannot change. Our task is to try to understand why the plot of Gibbs energy as a function

of composition has the form shown in Fig. 8.2 and also to identify the factors which influence the position of the minimum.

8.2

The equilibrium between two species

The simplest kind of equilibrium we can consider is when there is just one reactant (A) and one product (B):

A

= B.

The equilibrium between isomers (illustrated in Fig. 8.3) is an example of this kind of reaction.

H /\

2

H2C — CHs

—

cyclopropane

Let us imagine that A and B are both gases and that we start out with one mole of pure A sealed in a container such that the pressure is 1 bar (1 bar is 10° N m~?, very close to 1 atmosphere pressure). The reaction will come to

H

Hs“

voy

“CHa

propene

F

y N= N®

—= —

\ N=N =n" °

F

Fig. 8.3 Examples of equilibria involving just two chemical species which are isomers of one another.

equilibrium by some of the A converting to B, so we can specify the extent to which this has happened simply by quoting the percentage of B in the mixture. As the reaction involves no change in the number of moles, the pressure does not change as A and B interconvert. Figure 8.4 shows how the Gibbs energy varies with percentage of B. On the left we have pure A, and so, as there is one mole of A present, the Gibbs energy is the molar Gibbs energy of pure A, Gm(A). On the right we have pure

B, and so the Gibbs energy is just the molar Gibbs energy of pure B, Gm(B).

To draw the graph we have arbitrarily chosen G,,(B) to be less than G»,(A). The task now is to try to explain why the curve has this shape, and in particular

why it shows a minimum. Suppose we start with pure A and then allow a very small amount of A to convert to B; as a consequence there will be a small change in the enthalpy and in the entropy. We will concentrate on the entropy change which we can think

of as being due to two contributions. The first contribution comes from the fact that we have converted some A to B. Given that the two substances are likely to have different molar entropies, changing some A into B is surely going to result in a change in entropy. The second contribution comes from the mixing of this small amount of B into the bulk of A. So far we have not discussed this entropy of mixing, but you

The equilibrium between two species

115

Gibbs energy

——»

8.2

equilibrium

0

t

———_>

% of B

pure A

100

t

pure B

Fig. 8.4 Plot showing an example of how the Gibbs energy for the equilibrium between A and B varies with the composition, which in this case can be specified by the percentage of B. Arbitrarily, we have made the molar Gibbs energy of B lower than that of A.

can see that going from pure A to having a little B mixed in with A certainly gives rise to an increase in the entropy on the grounds that the mixture is more

‘random’ than pure A. We therefore expect this second contribution always to result in an increase in the entropy.

The first contribution might result in an increase or decrease in the entropy, but we argue that the entropy increase due to the second contribution — the one due to mixing — will always be dominant as there is a large increase in

randomness (that is, in entropy) on going from pure A to a mixture with a small amount of B in it. Given that AG

is defined as (AH

— TAS)

(p. 16), it follows that this

increase in entropy will lead to a decrease in the Gibbs energy. Therefore, as

we start from the left-hand side of the graph in Fig. 8.4 we expect the Gibbs energy to fall. Similarly, when starting from the right-hand side of the plot we can employ the same reasoning to argue that having a small amount of A mixed in with the bulk of B leads to an increase in the entropy and hence a decrease in the Gibbs energy.

Having now convinced ourselves why the Gibbs energy falls when we start

from either side of this plot, we now need to work out what happens in between. A simple argument is to note that as the Gibbs energy falls when we start from the left or right, for the curve to join up there must be a minimum somewhere between these two points.

To determine the exact form of the curve we need some more detailed ther-

modynamics, which we do not have time to go into here — so for now you will simply have to take the form of these graphs on trust.

. Locating the position of equilibrium The remarkable thing about the plot in Fig. 8.4 is that it turns out that the location of the minimum — that is the percentage of B present at equilibrium — depends only on the difference between the molar Gibbs energies of A and B.

Equilibrium

116

>

> @

c @ wn 2

2

Oo

0

——_

(c)

%

of B

100

0

(d)

%

of B

>

100

+— G,,(A) & oCc

G,,(B)

pp

oO en) 2

2

OO

—_——_S % of B

too

~2OsO

——_——_S % of B

Fig. 8.5 Illustration of how the position of equilibrium (indicated by the open arrow) is changing the relative molar Gibbs energies of A and B. In (a) Gm(A) and Gm(B) are equal, curve symmetrical and so the position of equilibrium lies at 50% B. In (b) Gm(A) is less than so the position of equilibrium lies towards A; in (c) Gm(A) has been reduced further and the therefore lies even further towards A. Finally, in (d), Gm(B) is less than Gm(A) and so the

T00 affected by making the Gm(B) and equilibrium position of

equilibrium lies towards B.

To prove that this is so needs a deeper study of the principles of thermodynamics than we have time to go into here, so we will simply have to take this result

on trust. Figure 8.5 illustrates how the position of the minimum shifts for different

values of Gm(A) and Gm(B). In (a) the molar Gibbs energies of A and B are equal; the minimum in the Gibbs energy of the mixture is at 50% B. In (b) the molar Gibbs energy of A is lower than that of B, and so the position of

equilibrium moves to the left, corresponding to the presence of more A than B;

in (c) the molar Gibbs energy of A is lower still, and this shifts the position of

equilibrium even further towards A. Finally, in (d) the molar Gibbs energy of B is lower than that of A so now the equilibrium lies towards B. We see that the position of equilibrium lies towards the species with the lowest molar Gibbs energy. If you take a piece of string or chain and hold one end in your left hand

and the other in your right, the string falls in a curve rather similar to those in

Fig. 8.5. The height of your left hand represents the molar Gibbs energy of A, and the height of your right hand represents the molar Gibbs energy of B. If you hold your two hands level, your will see that the string hangs so as to

make a minimum at a position midway between your hands: this is like plot

(a). If you lower your left hand, the minimum moves towards the left, just as

in plots (b) and (c). Conversely, if you lower your right hand, the minimum moves towards the right, as in plot (d). As you know, when a reaction has come to equilibrium, the concentrations

of products and reactants are related by the value of the equilibrium constant.

8.2

The equilibrium between two species

117

In the case of the equilibrium between A and B, the equilibrium constant, K, is

given by

_ (Blea [Aleq

where [A]eq and [B]eq are the equilibrium concentrations of A and B respec-

tively. If at equilibrium more B is present than A, K is greater than 1 and the

equilibrium lies towards the products.

Conversely, if the equilibrium lies to-

wards the reactants there will be more A present than B and the equilibrium constant will be less than 1.

The percentage of B at which the minimum Gibbs energy occurs deter-

mines the value of the equilibrium constant. We have already described how the location of the minimum is determined solely by the difference in the molar Gibbs energies of A and B. It therefore follows that the value of the equilibrium constant must be related to this difference, and some more detailed thermodynamics shows us that: Gm(B) — Gm(A) =

—RT Ink

(8.1)

where R is the gas constant (8.3145 J K—! mol~!) and T is the absolute temperature (in K). This equation has the correct form, as if Gm(B) is less than Gm(A), the

left-hand side will be negative and so In K will be positive. This means that K is greater than 1 so that at equilibrium the product B is favoured, as depicted in Fig. 8.5 (d). In contrast, if Gm(A)

is less than G»(B),

will be positive and so InK will be negative.

the left-hand side of Eq. 8.1

This means that K will be a

The surprising thing about Eq. 8.1 is that it tells us that the equilibrium constant depends only on the difference between the molar Gibbs energies of pure A and pure B. This really is quite a remarkable result and worth discussing a little more before we move on. Interpretation Suppose that Gm(B) is less than Gm(A). This means that if we start with pure A and convert all of it to B the process would be accompanied by a decrease

in Gibbs energy and therefore be spontaneous. This change in Gibbs energy is shown as AG, in Fig. 8.6. However, what we have seen is that there are some ratios of A to B for

which the mixture has lower Gibbs energy than either pure A or pure B; one of these mixtures has the minimum Gibbs energy and this is the one which corresponds to equilibrium. As is shown in Fig. 8.6, going from pure A

to the

equilibrium mixture involves a larger decrease in the Gibbs energy, AG2, than going to pure B.

Gibbs energy

fraction between 0 and 1, favouring the reactant A at equilibrium, as depicted in Fig. 8.5 (b) and (c).

0

—_———> %

of B

100

Fig. 8.6 The molar Gibbs energy of the product B is lower than that of the reactant A, so going frorn pure A to pure

B involves a decrease in the Gibbs energy (AG). However, for certain ratios of A to B the Gibbs energy of the mixture is /ower than that of pure B; the lowest

value of the Gibbs energy corresponds to the equilibrium point and moving to this point from pure A involves the largest decrease in the Gibbs energy (AG»).

Equilibrium

118

8.3

General chemical equilibrium A = B

‘These ideas about the simple

equilibrium are just a special case of a

more general result which is that for any reaction the equilibrium constant, K, is given by

A,G° = —RT Ink.

(8.2)

A,G° is the standard Gibbs energy change which can be computed from A,G°

=

A,H°

—_

TA,S°

(8.3)

where A,H° is the standard enthalpy change and A,S° is the standard entropy change for the reaction. The first thing we need to do is describe what we mean by a ‘standard change’. Standard states and standard changes

We first need to introduce the concept of a standard state; this is a particular state of the substance in question, defined according to the following agreed convention:

substance

standard state

gases

the pure gas at a pressure of 1 bar (10° N m7?)

solids

the pure solid

liquids

the pure liquid

solutions

— the solution at unit concentration

The standard state given in the table for a solution only applies to an ideal solution in which there are no solute—solvent interactions; for real solutions in which there are such interactions the definition is more complex and we shall

not go into this here. The standard state is denoted by a superscript ° or sometimes a Plimsoll line

e. It is sometimes thought, erroneously, that the standard state implies a certain temperature: this is not the case. In fact, when quoting values for standard enthalpy, entropy or Gibbs energy changes we must always state the temperature at which this value applies as these quantities are temperature dependent. Having introduced the standard state we can now define standard changes for reactions.

Such changes refer to a particular balanced chemical equation.

For example, A,G° for the reaction

Ho(g) + O2(g) —> H20(1)

(8.4)

is the change in Gibbs energy when one mole of H2(g) reacts with half a mole

of O2(g) to give one mole of H2O()), all of the species being present in their standard states and at the stated temperature.

It is very important to understand that the value of A,G° refers to complete

reaction, i.e. the hydrogen and oxygen must be converted completely to wa-

ter. Note too how the values of the stoichiometric coefficients come into the

definition of A,;G°.

8.3.

General chemical equilibrium

119

So, if we doubled the stoichiometric coefficients in Eq. 8.4 and wrote it as

2H2(g) + O2(g) —> 2H20(/) A;,G® would be the change in Gibbs energy when two moles of H2(g) react with one mole of O2(g) to give two moles of H2O(/). The numerical value of

A,G° for this reaction would be twice the value of that for Eq. 8.4. A second example is the formation of ammonia:

*N2(g) + 2H2(g) —> NH3(g) for which A;G° is the change in Gibbs energy when half a mole of No(g) reacts with 4 moles of H2(g) to give one mole of NH3(g), all in their standard states and at the stated temperature.

In many ways A,G° is a hypothetical quantity as it refers to the change in Gibbs energy when the reactants, in their standard states, are converted com-

pletely to products, also in their standard states. If we actually mixed the reactants together in their standard states there is no guarantee that the reaction

would go completely to products in their standard states. All that we can be sure will actually happen is that the reaction will go to its equilibrium position, which often will not involve complete conversion to products.

For example, at standard pressure and at room temperature not much ammonia will be formed by mixing Nz and H2. However, this does not stop us from imagining what the change in Gibbs energy would be if the reaction went completely from N2 and H2 to NH3.

The standard enthalpy change is defined in the same way as A,G°: for the

stated reaction it is the change in enthalpy when the reaction proceeds completely from reactants to products, all species being in their standard states.

Similarly, the standard entropy change is the change in entropy for this process. Returning to the simple equilibrium between A and B which was discussed

in Section 8.2 on p. 114, we can see that because we took the pressure to be 1 bar, the difference in the molar Gibbs energies of A and B is in fact the same thing as A,G° for the reaction; this is shown in Fig. 8.4 on p. 115. So, Eq. 8.1

is just a special case of Eq. 8.2. Determining standard changes The usual way of finding A,H° thalpies of formation,

A¢H°.

is to use tabulated values of standard en-

These are defined in such a way that for any

balanced chemical equation we can find A,H° by adding together the ArH values of the products and subtracting those of the reactants, taking into ac-

count the stoichiometric coefficients. For example, to find AgH°®

tion

for the reac-

SO2(g) + 202(g) — $O3(g)

we can imagine a Hess’ Law cycle in which the reactants are broken down

into their elements (in their standard states) and then these are re-formed to products:

120

Equilibrium

SOr(g) + 202g) “S SOs(g) —arH*(802)|

|

~earH*(02)|

Jareecsos)

elements in their standard states hy

A-H° is thus given by

|

ArH° = ArH°(SO3(g)) — ArH°(SO2(g)) — ArH? (O2(g)).

As you will recall, the standard enthalpy of formation of an element is zero, so in the above equation

ArH °(O2(g)) = 0.

Similarly, A,S° values are found by adding together the standard (absolute) entropies (S°) of the products and subtracting those of the reactants, taking into account the stoichiometric coefficients. So, for the above reaction:

A,S° = S°(SO3(g)) — S°(SO2(g)) — %S°(O2(g)). As with enthalpies of formation, extensive tabulations of standard entropies are available. Note that the standard absolute entropies of the elements are not zero. Having found A,H° and A,S° we then find A,G° using Eq. 8.3 A,;G°

=

A,H°

—_

TA,S°.

An example

Let us use this approach to find A,G° for

SO2(g) + 02(g) —> SO3(g). From tables we find (all at 298 K and for the gaseous state) AsH°(SO3) = —396 kJ mol! and ArtH°(SO2) = —297 kJ mol™!; so, remembering that ArH? for Oz is zero,

A,H® = Af¢H°(SO3(g)) — AgH°(SO2(g)) — AsH°(O2(g))

= —396 — (-297) —')» x 0 = —99 kJ mol~!.

The same tables give us the following standard entropies:

S°(SO3)

=

257

JK7! mol™!, S°(SOz) = 248 J K~! mol! and S°(O2) = 205 J K~! mol-!: so

A,S° = S°(SO3(g)) — S°(SO2(g)) — 45°(02(g)) = 257 — 248 — 'y x 205 = —93.5JK7! mot!.

These values allow us to find A,G° at 298 K:

A,G° = A,H° —TA,S°

= —99 x 10° — 298 x (—93.5)

= —71 x 10° J mol™!.

Next we will see what this implies for the value of the equilibrium constant.

8.3

General chemical equilibrium

121

Equilibrium constants The equilibrium constant and the standard Gibbs energy change for a reaction

are related according to Eq. 8.2

A,G° = ~RTInK which can be rewritten to give K as

A,G°

K = exp

RT

This relationship tells us that if A;G° is negative, the exponent (the expression

in the brackets) will be positive and so the equilibrium constant will be greater

than 1, i.e. the products are favoured. On the other hand, if A,G° is positive,

the exponent will be negative, giving an equilibrium constant of less than 1, which means that the reactants are favoured. These points are illustrated in

Fig. 8.7.

In the case of the formation of SO3 from SO, 298 K, AyG° = —71 x 10° J mol! and so K

= exp(

= exp

“reactants -

K=0

and O 2 we found that at

favour

negative

0

positive

A,G°——>

Fig. 8.7 Graph showing how the sign of ArG® affects the position of equilibrium. If ArG° is positive the equilibrium constant is less then 1 (but still positive) which means that the reactants are

favoured. If ArG®° is negative the equilibrium constant is greater than 1 and the products are favoured.

—A,G°

RT —(—71 x 103) 8.3145 x 298

= 2.29 x 10!2. The equilibrium constant is very large, implying that the equilibrium will be

totally in favour of the products in this reaction. Before we move on there is one point of possible confusion we need to clear

reactant, A. It therefore follows that the conversion of pure A to pure B (at standard pressure) will not take place as this would be accompanied by an

increase in the Gibbs energy. However, this does not mean that the conversion of some A to B is forbidden — far from it. We see this clearly in Fig. 8.8 where the conversion of pure A to the equilibrium mixture is accompanied by a decrease in the Gibbs energy,

even though A,G° is positive. So, if a reaction has a positive A,G° this does not mean that the reaction

will not take place; rather, it means that the reaction will come to an equilibrium position which favours the reactants. Similarly, a reaction which has a negative

A,G° will not go entirely to products, but it will go to an equilibrium position which favours the products.

In fact, because of the exponential relationship between A,G° and the equi-

librium constant, once A,G° becomes more positive than a certain value the equilibrium constant becomes so small that the equilibrium lies entirely to the

i=)

is positive, i.e. the pure product, B, is higher in Gibbs energy than the pure

Gibbs energy

up. In Chapter 2 we showed that a spontaneous process must be accompanied

by a decrease in the Gibbs energy, and we have used this criterion to discuss chemical equilibrium. Consider the situation shown in Fig. 8.8, in which A,G°

% of B

100

Fig. 8.8 Illustration of how a reaction which has a positive A;G°® still takes place to a certain extent, i.e. comes to a position of equilibrium in which some product is present. Going from pure A to pure B would involve an increase in the Gibbs energy and so is not allowed. Nevertheless, going from pure A to the equilibrium mixture involves a decrease in the Gibbs energy and so is allowed. A reaction with a positive A,G° is not ‘forbidden’ but simply comes to a position

of equilibrium which favours the reactants.

Equilibrium

122 we

8

10°97

wn

6 25 | 10°.

products}

favoured|

“

10 t

50

T

-40

T

-30

T

,

-20

!

3

AG? / kJ mor"

—_—____———

Ay

-10

T

)

10°35

10"

6

T

T

20

-

30

t

8640

1

50

reactants favoured

10°9 J

IN

Fig. 8.9 Plot showing how the equilibrium constant, K, varies with the standard Gibbs energy change of the reaction (ArG°) at a temperature of 298 K; note that the vertical scale is logarithmic. If ArG° is more negative than about —40 kJ mol~! the equilibrium constant is so large that essentially the conversion to products is complete. Similarly, if A;G° is more positive that about +40 kJ mol—! the equilibrium constant is so small that essentially no products are formed.

reactants, i.e. the reaction does not proceed to.a significant extent.

Similarly,

once A,G° is more negative than a certain value, the equilibrium constant becomes so large that to all intents and purposes the equilibrium lies entirely in favour of the products.

Figure 8.9 shows how K varies with A,G°; note that the vertical scale is logarithmic. We see from this plot that once A,G° exceeds around +40 kJ mol~! the equilibrium constant is so small that essentially none of the reactants have become products. On the other end of the scale, if A,;G° is more

negative than about —40 kJ mol~! the equilibrium constant is so large that to all practical intents and purposes the reaction has gone entirely to products. Finally, note that if A;G° = 0 the equilibrium constant is one, implying an equal

balance between products and reactants.

8.4

Influencing the position of equilibrium

For a given reaction the value of the equilibrium constant is fixed once we

specify the temperature and the states of the reactants (solid, liquid, gas, etc.). This section describes a number of ways in which the actual amount of products can be increased — in other words, how to increase the yield of the reaction,

something we often want to do for practical reasons.

Temperature

Both the equation relating A,;G° to the equilibrium constant A,G° = —RTInK

(8.2)

A,G° = A,H° — TA,S°

(8.3)

and the definition of A,G°

8.4

Influencing the position of equilibrium

123

involve temperature explicitly, so we can expect the temperature to have an influence on the value of the equilibrium constant. It turns out that the values of A,S° and A,;H° also depend on temperature, although not very strongly. Over a modest temperature range it is reasonable to assume that they are constant,

which is what we will do from now on. As both Eq. 8.2 and Eq. 8.3 are expressions for A,G° we can equate their right-hand sides to give —RTInK Dividing both sides by —RT

= A,H° —TA,S°.

gives

ArH? a(1\ A,S° InK =" R (;) TR

8.5

(8.9)

If the reaction is endothermic (A,H° is positive) the term (—A,H°/RT) is negative and so increasing the temperature makes it Jess negative. This means that as T increases both In K and K increase, as is illustrated in Fig. 8.10. In other words, for an endothermic reaction increasing the temperature shifts the

equilibrium towards the products.

If the reaction is exothermic (A,H° is negative) the term (—A,;H°/RT) is positive and so increasing the temperature makes it less positive. As a result

increasing the temperature makes both In K and K smaller (see Fig. 8.10). In

words, for an exothermic reaction, increasing the temperature shifts the equi-

librium towards the reactants.

You are probably familiar with these conclusions as they are often described as being a consequence of Le Chatelier’s Principle, one statement of which is that ‘the equilibrium shifts in order to oppose the change’. So, for

an endothermic reaction, an increase in the temperature is opposed by absorbing heat which means that the reaction must move further to products, i.e. the equilibrium constant must increase. Equation 8.5 puts this application of Le Chatelier’s Principle on a quantitative footing. We will look at two examples of the effect of temperature on the position of equilibrium. Dimerization of NO2 For our first example, let us look again at the dimerization of NO2(g):

2NO2(g) = N204(g). From tables, we find for this reaction that at 298 K,

A;

H° = —57kJ mol7! and

A-S° = —176J K~! mol~!. These values make sense as a bond is being made, so we expect the release of energy, and the reduction in entropy is associated with two moles of gas going to one. At 298 K we can compute A,G° and then K: A,G°

=>

A,H°

—

TA,S°

= —57 x 10° — 298 x (—176) — 46x

10° J mol7!.

In kK —~

This equation tells us that the way in which the equilibrium constant varies with temperature depends on A,H°.

exothermic

endothermic

T —, Fig. 8.10 Graph showing the different ways in which In K varies with temperature (as predicted by Eq. 8.5) for an exothermic and an endothermic

reaction. For an endothermic reaction

the equilibrium constant increases with temperature; for an exothermic reaction,

the opposite is the case. Thus, Eq. 8.5 is an expression of Le Chatelier’s Principle.

Equilibrium

124

K =exp

(“ar) 7

—~(—4.6 x 103)

= &P \ 33145 x 298 =63

”—

We see that A,G° is negative and so the equilibrium constant is greater than l,

showing that at equilibrium the products are preferred. However, A,G° is not

that negative and so the equilibrium constant is modest (6.3) which tells us that

although the equilibrium lies on the side of the products, there are still plenty of reactants present. As the reaction is exothermic, lowering the temperature will increase the

proportion of products. Let us repeat the same calculation at 273 K:

AG? = —57 x 103 — 273 x (176) = —9.0 x 10? J mol7!

oo

—(—9.0 x 103)

8.3145 x 273

The equilibrium constant is now much larger, meaning that at this lower temperature the proportion of dimer (N2Oq) present is larger than it was at 298 K. Repeating the calculation at 373

K gives

K =

0.062, showing that at this

higher temperature the fraction of dimer present is very small. These calculations illustrate very nicely how we can shift the equilibrium one way or the other simply by altering the temperature.

Extraction of metals Our second example is rather different, and concerns the commercially very important process of extracting metals from their oxides. Typically, this is done by heating the oxide with carbon which acts as a reducing agent, thus releasing

the free metal and forming CO or CO. The chemical processes involved are often fairly complex, but for a simple divalent metal oxide (general formula MO) we can get a flavour of what is going on by just considering the reaction

MO(s) + C(s) = CO(g) + M(s).

(8.6)

The following table gives thermochemical data (at 298 K) for C, CO, the metals copper, lead and zinc and their oxides. Cc ArH? /kJ mol7! S°JK~!mol7!

Co

Cu

-111 5.74

198

CuO

Pb

—157 33.2

42.6

PbO

Zn

—219 64.8

66.5

ZnO —348

25.4

40.3

Using these we can compute A,G° for the reaction of Eq. 8.6 at any temperature (provided we assume that A;H° and A,S° are not temperature dependent). The results for reaction at 1000 °C and 1500 °C are shown in the following table (you can check to see if you agree with the numbers); similar data are also shown in Fig. 8.11.

8.4

Influencing the position of equilibrium

oxide A;H°/kJ mol7! CuO PbO ZnO

at 1000 °C

A,S°/J K7! mol7!

46 108 274

125

A,G° /kJ mol7!

182 190 177

—186 —133 12.3

at 1500 °C

A,G° / kJ mol7!

—277 —229 -76.2

As expected, for all the metals the reaction has a positive A,S° resulting from the generation of one mole of gas on the right-hand side of the equation. The reactions are all endothermic which means that, as A;G° =

perature influences the equilibrium constant. Read casually, the previous para-

graph makes it sound as if it is the sign of A;S°

which determines how the

equilibrium will change with temperature. This is not what the paragraph says: what it says is that the sign of A, S° determines whether A,G° rises or falls with temperature, but A,G° is not the equilibrium constant. To find the equilibrium constant from A,G° we need to use A;G°

= —RT In K, a relationship which

introduces another temperature dependence; so knowing how A,G° varies with temperature is not the whole story. In fact, as we have seen, the effect of temperature on the equilibrium con-

stant is given by Eq. 8.5

ink A,H® nK =— R

(1 = T

n R

This shows that it is the sign of A;H° which determines how the equilibrium constant depends on temperature as it is A; H° which is multiplying the (1/7) term. So, although it is true that if A,S° is positive, increasing the temperature

will cause A,G° to decrease, to understand the effect of temperature on the equilibrium constant we need to look at the sign of A;H°. What the table tells us therefore is that as the reactions are all endothermic, increasing the

temperature will move the equilibrium to the products. This subtle point about the temperature dependence does not alter the basic idea that if A,G° is substantially negative the position of equilibrium will lie almost entirely toward the products. At 1000 °C, A,;G°® is substantially negative for copper and lead, showing that metal + carbon monoxide will be formed. However, for zinc A,G° is positive at this temperature, which tells us that the equilibrium will favour the reactants (ZnO + C) and so zinc metal will

not be extracted. In order for the reduction to produce zinc we have to raise the temperature higher, and we can see from the table that at 1500 °C,

A,G°

is now

substantially negative for the ZnO reduction. We therefore conclude that to obtain copper or lead from their oxides, reduction with carbon at a temperature of 1000 °C will be sufficient, but to obtain zinc from its. oxide a substantially higher temperature will be needed. Figure 8.11 presents the results in a slightly different way, and from this graph we can see that for Zn the switch over from a positive to a negative A,G° occurs at around 1100 °C. In practice we need to

G°/kJ mol"!

A,H° — TA,S°, a negative value of A;G° can only be achieved by a positive A,S° (which is what we have here) and a sufficiently high temperature that the —T A,S° term is dominant. We need to be careful here not to fall into making an error about how tem-

1000 100

1200 +

T/°C 1400 =

1600 ;

OF

-100

©. -200 — -300l

ob Cu

Fig. 8.11 Plot showing how the standard Gibbs energy change for the reaction of Eq. 8.6 varies with temperature for three different metals; the process will only be successful if A; G° is significantly negative. It is clear, therefore, that the extraction of Zn requires a higher temperature than for Cu or Pb. The values of ArG° have been computed assuming that A,H® and A,S° are independent of temperature, and so the plots are straight lines.

Equilibrium

126

be at a higher temperature than this to ensure that A;G° is sufficiently negative for the equilibrium to favour products strongly. Concentration The value of the equilibrium constant determines the ratio of the concentrations of products and reactants, and this has a fixed value at a particular temperature.

However, we can influence the actual concentration of a product by altering

the concentrations of the other species. How this works is best illustrated by an example, such as the equilibrium shown in Fig. 8.12 which is the reaction used to form an ester (E) from an alcohol (A) and a carboxylic acid (C).

O

H3C~

I Cc

OH

+

fe)

CH3OH

HaC~

A

I

E

OCH

+

0

Fig. 8.12 An ester, E, is formed from the reaction between a carboxylic acid, C, and an alcohol, A; water is also produced in the reaction. Here the reaction is between ethanoic (acetic) acid and methanol to give methyl ethanoate (methyl acetate).

The equilibrium constant, K, for this reaction is given by: [EJeqlH2O0 Jeq

K = ——————_

[CleglA leq

8.7

7)

where [E]eq means the equilibrium concentration of the ester, and so on. Remember that at a particular temperature the value of K is fixed, so the concentrations of the four species must adjust themselves so that the ratio on the

right-hand side of Eq. 8.7 is equal to the value of K.

Suppose we let the reaction come to equilibrium, but then by some means

we Start to remove one of the products (say the ester); what will happen? The moment the concentration of the ester falls the ratio on the right-hand side of Eq. 8.7 will be too small; to restore it to the correct value we have to either

increase the amounts of ester and water or decrease the amounts of carboxylic acid and alcohol.

Both of these things are achieved if some of the acid and

alcohol react to give more water and ester. So, by removing the ester we disturb the equilibrium in such a way that the only way it can be restored is for more ester to be produced; we say that the reaction has been ‘forced to the right’ by removing the product. For the

particular reaction shown in Fig. 8.12 it turns out that the ester is more volatile

than any of the other species, so it can simply be distilled off constantly forcing the reaction to the right and so increasing the yield of the ester.

Another way of forcing the reaction to the right is to add more of one of the reactants. Once again, this reduces the value of the ratio on the right-hand side of Eq. 8.7 and so to restore the correct value some of the alcohol and carboxylic acid have to react to form more ester. If the alcohol is a simple one, such as methanol, we would probably use it as the solvent for the reaction, thus ensuring that its concentration was very high.

A similar example is in the formation of an imine from the reaction of a ketone with an amine, Fig. 8.13. In this reaction water is produced on the righthand side of this equilibrium and so the yield of the imine can be increased by

8.4

Influencing the position of equilibrium

127

removing the water. This can be achieved by adding a solid material known as

a molecular sieve which is a special kind of zeolite clay which has cavities into

which water will bind tightly. This effectively removes the water, so forcing the reaction to produce more of the imine in an attempt to restore the equilibrium.

H3C

H3C

\

jf

°

+

CHs3NH,

H3C

\

C=N

/

CH3 +

H2O

H3C ketone

imine

Fig. 8.13 An imine is formed from the reaction of a ketone and an amine.

We can use the same strategy to shift the reaction the other way; suppose,

for example, we want to hydrolyse an ester back to the alcohol and the carboxylic acid — this is the reverse reaction shown in Fig. 8.12. To force the reaction to the left, we need to increase the amount of the species on the right and this is easily done by making water the solvent. Now its concentration will

be very large, and so the reaction will be shifted to the left, in favour of the

hydrolysed products.

The formation of an acetal from the reaction of a ketone with an alcohol,

shown in Fig. 8.14, is an equilibrium reaction which we sometimes want to force one way and sometimes the other. H3C

H3C

H3C

= ‘C=O / ketone

++ CHOH °

H3C

+ So Oso 1“ Nocu 2 3

acetal

Fig. 8.14 The formation of an acetal from a ketone and an alcohol is a readily reversible reaction which we can ‘force’ one way or the other by altering the conditions.

If we wish to form the acetal we use the alcohol as the solvent a dehydrating agent — both choices force the equilibrium to the right. other hand, if we wish to regenerate the ketone from the acetal, we reaction in aqueous solution so that the excess of water will force the to the left.

and add On the run the reaction

The Haber process Our final example is the formation of ammonia from hydrogen and nitrogen (the Haber process):

No(g) + 3H2(g) = 2NH3(g) which is the way in which millions of tonnes of ammonia are synthesized each year. In order to make the reaction go at a reasonable rate temperatures of around 400 °C are needed together with a solid iron oxide catalyst. Unfortu-

nately, the reaction is exothermic (A;H° = —92 kJ mol—!) so raising the temperature shifts the equilibrium towards the reactants (Section 8.4 on p. 122); it

is found that at this high temperature the equilibrium constant is about 10-2.

Equilibrium

128

The strategy for increasing the yield of ammonia is simply to remove the

ammonia and then let the nitrogen and hydrogen come back to equilibrium,

H, and N, in

thus generating more ammonia.

In practice this is done by passing the gases

iN

Y

reaction chamber

(catalyst at 400 °C)

unreacted H, and N,,

over the catalyst so that they come to equilibrium, then separating out the ammonia and finally recycling the unreacted gases back over the catalyst; the

cooling chamber

process is illustrated in Fig. 8.15. Removing the ammonia is quite easyas ammonia will liquefy at a temper-

ature (around —35 °C) well above the temperature at which either nitrogen or

hydrogen will liquefy.

So, simply by cooling the gases the ammonia can be

separated as a liquid. Coupling reactions together Suppose that the reaction we are interested in has a positive

A;G°,

which

means that the equilibrium constant will be less than 1, and very little of the products will be formed. One way to force the formation of larger amounts of the products is to ‘couple’ the reaction to another reaction which has a negative A,G° so that, when taken together, the overall A,G° is negative. What we are doing is driving the reaction with the unfavourable A,G° using a reaction with a favourable A,G°. For the two reactions to be coupled in this way they must be able to influ-

liquid NH, Fig. 8.15 Simplified picture of the arrangement for the Haber process for synthesizing ammonia. After coming to equilibrium over the catalyst, only a small fraction of the hydrogen and nitrogen has

been converted to ammonia. The ammonia is separated from the other

gases by liquefying it, and the unreacted

nitrogen and hydrogen are returned to the reaction chamber.

ence one another; having the reactions take place in separate beakers on the bench or simply mixing all the reagents together will not achieve the required coupling. In Nature this coupling is achieved using enzymes which control and direct the chemistry, and indeed very many of the important chemical pro-

cesses of life are driven by this kind of coupling. We do not have time here to go into the details of exactly how enzymes achieve this coupling, but will just illustrate the outcome for one very fundamental reaction in living systems

— the formation of the peptide bond. In living systems, proteins are synthesized by the polymerization of amino acids into long chains. The key reaction in forming the chain is for amino acids to condense together by forming peptide bonds, as shown in Fig. 8.16 for the formation of a dipeptide. O R

le

“CH”

c

amino

O

OH acid

* 1

HoN

CH”

,

amino

:

NH>

OH

Ro

acid 2

al

O

NBR

N

bt

CH™

oH * 420

dipeptide

Fig. 8.16 Two amino acids condense together to form a dipeptide, and in doing so form the -CONH— peptide bond, shown in the grey box. Different amino acids have different side groups, R and R’.

This reaction has a rather unfavourable A,G° of +17 kJ mol7! and so at equilibrium very little of the dipeptide will be formed. To get round this, Nature couples this reaction with the hydrolysis of adenosine triphosphate (ATP) to

adenosine diphosphate (ADP):

ATP + H20 —> ADP +

inorganic phosphate.

8.4

Influencing the position of equilibrium

This reaction has a very favourable A;G°

129 of —30 kJ mol~!,

sufficiently

negative to outweigh the positive A,G° for the formation of the peptide bond.

So, taken together the two reactions have an overall negative A,G° making the formation of the peptide bond thermodynamically feasible. Nature frequently uses the hydrolysis of ATP to ADP to drive reactions which have unfavourable (positive) values of A,G°, and so ATP is often regarded as the source of the energy which drives the chemistry of life. We can now see that by ‘energy’ we really mean Gibbs energy, as this is what

drives reactions forward. So, when biochemists describe ATP as a high energy molecule, what they mean is a high Gibbs energy molecule. For all of this to work, the cell has to be able to make ATP, for example

from ADP by running the hydrolysis reaction backwards: ADP +

inorganic phosphate —>

ATP + H20O

but this reaction has an unfavourable A,G° of +30 kJ mol7! and so will not go on its own. As with peptide bond formation, Nature drives the formation of

ATP by coupling it to another reaction, such as the oxidation of glucose. This oxidation is often described as the fundamental source of ‘energy’ for many living systems, including ourselves. The overall reaction is C6H1206 + 602 —>

6CO2 + 6H20

and this has a very large negative A,G° of —2880 kJ mol7!.

In Nature the

oxidation of one molecule of glucose is coupled by a very complex series of

enzymatically controlled reactions to the formation of around 38 molecules

of ATP from ADP, and in this way the high energy ATP molecules needed in many other processes in the cell are generated. We obtain sugars, such as glucose, from plants which synthesize them from

carbon dioxide and water, releasing oxygen in the process. The formation of glucose in this way is simply the reverse of the oxidation given above: 6CO?7 + 6H20 —

C6H120¢6 + 602.

However, this reaction has a very large positive A,G° so how can it be made to

go? The answer is that plants utilize the energy from light, in a process known

as photosynthesis, to force this reaction. A very complex and subtle series of processes and reactions are used to harvest the energy from light and utilize

it to form glucose — Nature has perfected this scheme over the millennia of evolution that have led to the green plants we know today. The coupling of an unfavourable reaction to a favourable one is absolutely crucial in the chemistry of life. We can only marvel at the subtle and efficient way in which Nature is able to achieve this coupling.

Equilibrium

130

8.5

Equilibrium and rates of reaction

Suppose that we have an equilibrium between reactants A and B and products C and D:

A+tB2=C+D. Let us start out with just A and B mixed together; they will react at some rate

to generate some of the products C ajd -D. However, the moment these are

formed they will start to react together and, via the reverse reaction, regenerate

the reactants A and B. The more of the products C and D that are formed, the faster the reverse

rate becomes; in contrast the more of the reactants A and B that are used up the slower the forward rate becomes. We know that eventually we will reach the

equilibrium point at which the concentrations are all constant — what must have

happened therefore is that the rates of the forward and reverse reactions have

become equal. When this is the case, as fast as A and B are removed by the forward reaction they are replenished by the reverse reaction in such a way that their concentrations do not change. Equilibrium is thus a dynamic situation — it 1S not that the reactions have stopped, it is just that the rate of the forward

and back reactions are equal so that it appears that nothing is happening. This brings us on to the whole topic of the rates of reactions — something which we have been carefully ignoring, or at least sidestepping, up to now. The problem is that even if a reaction is favourable in thermodynamic terms, i.e. has a large negative A,G°, this does not guarantee that the reaction will actually

take place at a measurable rate. For example, the oxidation of glucose is accompanied by a very large negative A,G° of some —2880 kJ mol~!, yet we can go out and buy glucose

powder safe in the knowledge that it will not burst into flames spontaneously. The reaction is thermodynamically feasible, but kinetically very slow. Other reactions are both thermodynamically feasible and fast. For example,

the neutralization of acids and bases (essentially the aqueous phase reaction H30* + OH~ —> 2H20) is both thermodynamically feasible and very fast. Even reactions in which the position of equilibrium lies close to the reactants

can come to equilibrium quickly.

For example, the dissociation of ethanoic

(acetic) acid has an equilibrium constant of only

107°

but nevertheless the

equilibrium is established very quickly once the acid is dissolved in water.

Reactions involving fons — particularly if they are oppositely charged as in the case of the neutralization of acids and alkalis — tend to be quite fast, and

similarly reactions involving simple proton transfer (for example from ethanoic acid to water) are often rapid. However, reactions involving the breaking and

making of bonds (say to carbon) are likely to proceed much more slowly.

In the next chapter we will look at the factors which control the rates of

reactions and then go on to see what a study of reaction rates can tell us about

the mechanism of a reaction.

9

Rates of reaction

At the end of the previous chapter we commented on the fact that just because a

reaction has a favourable A,G° (i.e. the position of equilibrium lies well to the products) this does not necessarily mean that it will proceed at a measurable rate. In this chapter we will look at the factors which determine the rates of

reactions and how we can influence these.

This is clearly a matter of great

importance if we actually want to do some practical chemistry, as well as being a rather fundamental aspect of chemical reactions. The second part of this chapter will move on to discuss how the study of reaction rates can give us information about what is going on in a reaction,

particularly when the reaction involves more than one step. This is the experimental study of reaction mechanisms.

9.1

What determines how fast a reaction goes?

In this section we will focus on a particular reaction (one you have seen before

on p. 108) which is the nucleophilic substitution of Br~ by OH”, Fig. 9.1. Each factor which influences the rate will be considered in turn. H.H

HO°

+

jo— Br

HH

—»

H Fig. 9.1 The nucleophilic substitution of OH

HO-—C

\

+

Br

H

for Br-; here CH3Br is transformed into CH3OH.

The molecules must collide

For there to be a reaction it is pretty obvious that the molecules must come close enough for them to interact — in other words they must collide. So we expect the rate of reaction to depend on the number of collisions per unit time, that is the rate of collisions.

In a gas or liquid the molecules are in a constant state of motion as a re-

sult of their thermal energy; they are rushing around in random directions, colliding with one another and hence changing their direction and speed. We therefore expect that the rate of collisions will depend on the concentration of the molecules, the speed at which they are moving and their size. The rate of collisions between two different species, A and B, will clearly go up as the concentration of either of them increases, simply because as an A molecule rushes around the chance that it will encounter a B molecule goes up

as the number of such molecules increases. It does not seem unreasonable that the rate of A—B collisions is proportional to both the concentration of A and that of B: rate of A-B collisions « [A] x [B].

132

Rates of reaction

The second thing which affects the rate of collisions is the speed at which the molecules are moving: we argue that the faster the molecules move the more likely they are to collide.

As you may know, there is a distribution of

speeds with which the molecules move, but the majority of molecules are

moving at speeds which are not that far from the average. In a gas, this average speed increases as the temperature increases; this is hardly a surprise as

increasing the temperature of a gas increases its energy which appears in the

form of kinetic energy — the molecules therefore move faster.

The final factor which determines the collision rate is the size of the

molecules: the larger they are the more chance there is of them colliding and so the higher the collision rate. For simple molecules in the gas phase we can use gas kinetic theory to

estimate the number of collisions as being around 102’ per second in a vol-

ume of 1 dm? at room temperature and pressure — a very large number by any standards. In liquids the situation is more complex because we also need to consider the rate at which the reactant molecules diffuse together; however,

once in proximity the collision rate between two molecules is even greater than in a gas. The molecules must collide with the correct orientation

As we discussed on p. 109, for the reaction shown in Fig. 9.1 to take place the nucleophile (OH™~ ) must approach the carbon from the opposite side to the

Br; this requirement is dictated by the nature of the HOMO and LUMO which

are involved in the reaction. Only a fraction of the total number of collisions between CH3Br and OH™ will have this correct orientation.

We have also seen that the attack on a carbonyl! group by a nucleophile has

a strongly preferred geometry (Fig. 7.16 on p. 105). Indeed it is common for

reactions to require the reactants to approach in a particular orientation — we

call this the steric requirement of a reaction. We can also expect that the larger and more complex a molecule becomes,

the smaller the fraction of collisions with the correct orientation will become. For example, it would not be unusual for only | in 10° collisions to have the correct geometry. There must be sufficient energy in the collision to overcome the energy

‘ barrier For the vast majority of reactions there is an energy barrier, which is a min-

imum amount of energy that two colliding molecules need in order to react;

simply colliding with the correct orientation is not sufficient — the molecules

must bring with them sufficient energy to cross this barrier.

This energy comes mainly from the collision of the two molecules. Each

has a certain kinetic energy as a result of its thermal motion — some molecules have more than the average energy and some less. So, some collisions will

have higher energy than others, and it is the ones which have an energy which is high enough to overcome the barrier that can lead to reaction. Typically, the energy barrier for a reaction is between 10 and 100 kJ mol.

At room

temperature

the average

thermal

energy

of a molecule

is around

4 kJ mol~!, so you can see that only those molecules whose energy is very

9.2

Why is there an energy barrier?

133

much greater than the average are likely to have enough energy to react when

they collide with another molecule.

The fraction of molecules with energies

much greater than the average is very small, so that typically only 1 in 10° molecular collisions has sufficient energy to overcome the barrier. Our picture of the reacting molecules is of there being many collisions between the reactants but of these only a minuscule fraction have the correct

orientation and sufficient energy to lead to products. A reactive encounter be-

tween molecules is thus a very rare event.

9.2

Why is there an energy barrier?

The presence of an energy barrier means that even if the products have lower energy than the reactants, the energy of the reacting molecules must first go up as they start to rearrange themselves into product molecules. Once this rear-

rangement has proceeded to a certain extent the energy starts to fall, eventually reaching the energy of the product molecules when they are fully formed.

this and has the

Figure 9.2 shows a mechanical analogy which is helpful in understanding concept of an energy barrier. We start with a block stood on its short side then try to push it over so that it lies on its long side. The end position lower (gravitational) potential energy than the starting position, but to push block over we first need to tilt it on its edge and in doing this the centre

of gravity rises, thus increasing the potential energy. Only when the tilt is far enough will the block fall over and reach the low-energy position. Like a chemical reaction, this system has to first go to a state of higher energy before it can reach the state with the lowest energy. (a)

(b)

(c)

(d)

Fig. 9.2 Pushing a block over from position (a) to (d) results in a reduction in the (gravitational) potential energy as the centre of mass (indicated by the dot) is lowered. However, to get the block to topple over it first has to be tilted on its edge, as shown

in (b) and (c). This raises the centre of mass and so

the energy goes up; only when the block is past position (c) does the energy go down. This process is an analogy for a chemical reaction: the products are lower in energy than the reactants, but to get between the two the energy must first rise; in other words there is an energy barrier which has to be overcome.

A simple example of such an energy barrier occurs in inversion of ammo-

nia, described on p. 87 and illustrated in Fig. 9.3. What happens here is that the

molecule is going from a trigonal pyramidal geometry with the hydrogens on

one side to an identical, mirror image, geometry with hydrogens on the other side; the whole process is rather like an umbrella being blown inside out. We can measure the progress along this route by giving the H-N-H bond angle;

Rates of reaction

134

this starts at 107°, goes to 120° at the planar geometry and then reduces back to its original value as the hydrogens move to the other side of the molecule ‘and end up in mirror image positions. We know that the equilibrium geometry of ammonia has an H-N-H bond angle of 107°, which means that this is the bond angle which gives the lowest energy; as the bond angle opens out the energy must therefore increase, as H

H

Hy \

N

4 H

H x

:

[: HH

trigonal pyramidal!

planar

UH

\H

trigonal pyramidal

shown in Fig. 9.3. Our interpretation of this is that the overlap of the orbitals is less than optimum as we move away from a bond angle of 107°, and so the

energy increases. The symmetry of the problem dictates that the highest energy point is when the bond angle is 120°, as this lies midway between the two trigonal pyramidal

geometries.

The species at this highest energy point is called the transition

energy

state; in this case it is an ammonia molecule with a planar geometry. For the reaction of Fig. 9.1 we can trace out how the energy varies as the

reaction proceeds from reactants to products just as we did for the inversion

107°

120°

—§\|{*—__

107°

H-N-H bond angle Fig. 9.3 In the inversion of ammonia the progress from the equilibrium trigonal pyramidal geometry to its mirror image is

characterized by the H-N-H bond angle. A plot of the energy against this angle

shows a maximum at 120°; this corresponds to the planar transition state.

of ammonia. However, for this reaction the progress from reactants to products cannot be specified by a single angle since as the reaction proceeds several bond angles as well as internuclear distances are changing. So, we plot the energy against what is called the reaction coordinate which is a complex combi-

nation of distances and angles, the precise definition of which need not concern us; all we need to know is that this coordinate starts at the reactants and ends

at the products. The plot of energy against reaction coordinate is known as an energy profile for the reaction; such a profile for the nucleophilic substitution reaction is shown in Fig. 9.4. reactants

HO"

©

H

\

+ c—Br Hd H

transition state

,

HO- -C- -Br ~L

HH

©

products /

Ho—c,,

H

‘H

+ Br®

H

Pal

ou o

jm

oD

——_—__>

reaction coordinate

Fig. 9.4 Energy profile for the reaction shown in Fig. 9.1; the reactants appear on the left and the products on the right. At the energy maximum is the transition state, a suggested structure for which is shown; there are partial bonds (shown dashed) to the OH and Br. The products are shown as having lower energy than the reactants, and so the reaction is exothermic; nevertheless, there is still an energy barrier to be overcome in going from reactants to products.

9.3

Rate laws

135

At the top of the profile there is a suggestion as to what the transition state might look like. The carbon atom is five-fold coordinated with partial bonds to both the incoming OH™ and the departing Br~. Over the course of the reaction, the hydrogen atoms have to move from one side to the other and so

in the suggested structure we have shown them in the same plane as the carbon

atom. It is important to realize that there is no way we can guess at the precise structure of the transition state — all we can do is to speculate about its general

form. It is clear from these pictures why the energy has to rise when the transition state is formed. The bonding is far from optimum — not least because there are five groups around the carbon; in addition, there are partially made bonds to the OH and the Br. This unusual geometry and the presence of partial bonds

is typical for a transition state; it is not surprising, therefore, that its energy is higher than that of the reactants. It is very important to realize that the transition state is not a real molecule: we cannot isolate it or study its physical or chemical properties. Rather, it is just a transient arrangement of the atoms through which the reaction passes on its way to products. The transition state has a fleeting existence, perhaps having a lifetime of 10~!? s or even less. Reactions with no barrier

The usual situation is for reactions to have a barrier, but there are some that do not. A typical example is the reaction in the gas phase between oppositely charged ions, such as:

Lit + FF” — LiF.

In this case we can attribute the lack of a barrier to the fact that the oppositely charged reactants attract one another and also that in going to the products no

bonds are broken. A second example involves the gas-phase recombination of radicals: *CH3

+

°CH3

—

CH3—CHs3.

We can attribute the lack of a barrier here to the fact that a bond is being made

and none broken. The C-H bonds only have to adjust themselves in a minor way to accommodate the new bond.

9.3

Rate laws

We described on p. 131 how the rate of collisions between two molecules A and B is expected to be directly proportional to the concentration of each. So,

if our nucleophilic substitution reaction (Fig. 9.1) really does take place by the OH™ and the CH3Br colliding in a reactive encounter, we would expect to find

that the rate of reaction is proportional to the concentration of each of these

species. Experiment confirms this expectation; it is found that rate of reaction =

K[OH” ][CH3Br].

This is called the rate law for the reaction.

(9.1)

Rates of reaction

136

[OH"] | :

time

time

Fig. 9.5 Plots of the concentration of the reactant OH~ and the product Br- as a function of time for the reaction of Fig. 9.1. Note how the concentration of the reactant falls towards zero and that of the product rises. Also shown as dotted lines on the left-hand plot are tangents to the curve; these give the slope of the curve which is the same thing as the rate. The way in which the absolute value of the rate falls as time increases can clearly be seen. In drawing these plots it has been assumed that at time zero the two reactants have the same concentration and that the concentrations of the products

are zero.

In the rate law k is the rate constant for the reaction; its value depends on all of the factors described in Section 9.1 (p. 131 onwards) apart from the

concentration, i.e. the size of the molecules, the speed they are moving at, and the fraction of collisions with the correct orientation and sufficient energy to overcome the barrier. The value of k has to be determined experimentally and it is usually found that it depends strongly on temperature, as will be discussed in the next section. The rate of reaction is how the concentration varies with time: rate of reaction =

change in concentration during time interval Ar

At

the dimensions of the rate are thus concentration x time~!. The concentration

of any of the reactants or products can be used to specify the rate. However, if we use a reactant whose concentration decreases with time, the rate will

be a negative quantity; in contrast, if we use a product whose concentration increases with time, the rate will be positive. Looking at the rate law, Eq. 9.1, we can see that at the start of the reaction

the rate will have its highest (absolute) value. As the reaction proceeds, the amount of the reactants OH~ and CH3Br decreases, and so the rate decreases,

eventually reaching zero at infinite times.

Figure 9.5 shows plots of how the

concentration of the reactants and products varies with time for this reaction.

The slope of a tangent to the curve gives us the rate at any time: this is because the slope is the change in concentration over the change in time, which is precisely the same thing as the rate. In Fig. 9.5 we see that for the plot of

[OH™] the slopes are negative, as expected for a reactant, and that as time proceeds the slopes are becoming less negative, i.e. the rate of the reaction is falling.

Order Another way of writing the rate law of Eq. 9.1 is

rate of reaction = k[OH™ ]![CH3Br]!

9.4

The Arrhenius equation

137

where we have raised the concentrations to the power of 1. Of course this is rather superfluous as [OH~]! means exactly the same thing as [OH]. However, the notional presence of this power in the rate law allows us to define something called the order.

The order is the power to which the concentration is raised in the rate law. So, in the above rate law the order with respect to OH™ is |, and similarly the

order with respect to CH3Br is also 1. We can also define an overall order, which is the sum of the orders of each species present in the rate law. So for

this reaction the overall order is 2.

An order of 1 is often called first order and an order of 2 is called second order. Thus the rate law for the reaction between hydroxide and bromomethane

(methyl bromide) can be described as being first order with respect to hydroxide and bromomethane and second order overall.

9.4

The Arrhenius equation

The rate constant generally depends quite strongly on temperature, and exper-

imental studies have shown that this temperature dependence often obeys the Arrhenius equation: k=

—E,

Aexp(Fa).

(9.2)

In this equation A is the pre-exponential or A factor, E, is the activation energy

and, as usual, T is the absolute temperature and R

is the gas constant.

This

its value it is essential to state the temperature at which the measurements were made. The interpretation of this equation is that the activation energy is the height of the energy barrier over which the reactants must pass — to be specific, it is the energy difference between the reactants and the top of the barrier (the transition state), as shown in Fig. 9.6.

energy

strong temperature dependence of the rate constant means that when quoting

From gas kinetic theory it can be shown that the fraction of collisions with energy greater than or equal to E, is given by exp(— £,/RT) and, as we dis-

cussed on p. products. We tion as arising the barrier. If there is

132, only these collisions are energetic enough to give rise to therefore interpret the exponential term in the Arrhenius equafrom the fraction of collisions with sufficient energy to pass over no energy barrier all of the collisions have sufficient energy to

become products; in mathematical terms if E, = 0 the exponential term, which is the fraction of collisions with sufficient energy, becomes 1. Under these circumstances the Arrhenius equation (Eq. 9.2) tells us that the rate constant is equal to the pre-exponential factor, A. So, we can interpret the value of A as

giving the rate constant in the absence of an energy barrier to reaction.

From the discussion in Section 9.1 (starting on p. 131) we can see that

the factors which contribute to the value of A are: the fraction of collisions which have the correct geometry, the size of the molecules and the speed with which they are moving. As we noted, this last factor depends on temperature but it turns out that this dependence is much weaker than that due to the

——\¥\¥—__

reaction coordinate Fig. 9.6 The activation energy, Ea, is the difference in energy between the reactants and the top of the barrier, i.e.

the transition state. For reaction to take place, the molecules must collide with at least this much energy and from gas

kinetic theory we can show that the fraction of collisions satisfying this requirement is exp(—Ea / RAT).

Rates of reaction

138

increasing E,

k A

ann

a

increasing T

A

ee

a

OL ——

0

cE

-

a

Fig. 9.7 Plot (a) shows the Arrhenius equation (Eq. 9.2) prediction for the variation of the rate constant, k, with temperature, T. The three lines are computed assuming the same value of the A factor but different values of the activation energy; the darker the line the larger the activation energy (the temperature scale does not start at zero). At high enough temperatures, the rate constant will reach the value of the pre-exponential factor, A; for the curves shown here the temperature is well below this limit. Plot (b) shows the variation of the rate constant, k, with activation energy, Ea; the three lines are computed assuming the same value of the A factor, but different temperatures; the darker the line the higher the temperature. Note how the rate constant responds rapidly to changes in the temperature and the activation energy.

exp(—E,/RT)

factor in the Arrhenius equation.

So, to a reasonable approxi-

mation we can assume that the A factor is temperature independent.

Figures 9.7 (a) and (b) show the predictions from the Arrhenius equation (Eq. 9.2) for how the rate constant varies with temperature and activation energy, respectively. The plots show how the exponential term makes the depen-

dence of the rate constant on the values of these two parameters rather strong.

We can turn the Arrhenius equation into a straight line plot by taking (natural) logarithms of both sides:

k=A

“t— InA

increasing E,

hence

exp

—E,

RT

Ink =InA+

—E,

R

1

—)}.

T

So, a plot of Ink against 1/T will be a straight line with slope (—E,/R);

the

intercept with the vertical axis, when 1/T goes to zero, will be In A. Figure 9.8 shows examples of this straight line plot; note how increasing the activation

e)

energy results in a more negative slope. 1/T

Fig. 9.8 An Arrhenius plot of In k against (1/T) which, as explained in the text, is

expected to give a straight line. The three lines are computed assuming the same value of the A factor but different values of the activation energy; the darker the line the larger the activation energy.

As

the slope of the line is —Ea/FA the greater the activation energy the more negative the slope. The intercept with the vertical

axis (when 1/T goes to zero) gives In A; this extrapolation is shown by dotted lines.

We can interpret the intercept with the vertical axis in the following way: when the temperature becomes very high, i.e. when 1/T goes to zero, each collision is sufficiently energetic to overcome the barrier and so each leads to reaction. The rate constant then has the value A because, as we noted before,

this is the value of the rate constant in the absence of a barrier.

For most

reactions this limit in which the rate constant becomes equal to the A factor

occurs at such high temperatures that either the reactants will have dissociated into atoms or other reactions will have taken over. The limit is therefore of theoretical, rather than practical, interest.

Given some experimental data of rate constants at different temperatures we can determine E, andA by plotting Ink against 1/7, just as in Fig. 9.8. The

9.5

Elementary and complex reactions

139

slope is (— E,/R) and the intercept with the vertical axis is In A. In practice, the range of temperatures over which data is available is usually rather limited so a long extrapolation is needed to find In A, making this value rather inaccurate.

9.5

Elementary and complex reactions

There is plenty of experimental evidence which leads us to believe that the

nucleophilic substitution reaction:

OH” + CH3Br —> CH30H + Brreally does take place as it is written, i.e. the products are formed directly from a single reactive encounter between an OH™ ion and a CH3Br molecule. There are many other reactions for which the experimental evidence is that they take place as written. For example, the two gas-phase reactions:

Cl + 03 ClO

—> ClO + O2

+ O —> Cl+ 02

which are key reactions in the destruction of atmospheric ozone by halogens,

are thought to proceed as written. On the other hand, there are reactions which certainly do not take place as written. For example, the gas-phase reaction between H2 and Brz has the stoichiometric equation H>. + Bro —>

2HBr

but there is much experimental evidence that the reaction does not occur by a single reactive encounter between an H2 and a Br2 molecule. Similarly, the oxidation of glucose in living systems has the overall stoichiometry CgH1206 + 602 —> 6CO2 + 6H20

but certainly does not take place by one molecule of glucose reacting directly with six of oxygen! What we are describing here is the distinction between an elementary and a complex reaction. An elementary reaction is one which we believe to take place in a single encounter and as the chemical equation is written. For example, the gas phase reaction between a hydrogen atom and Br2 written as H+Br2

—

HBr+

Br

is elementary and so takes place in a reactive encounter between an H anda Br2 molecule.

Complex reactions take place by a set of elementary reactions, called a mechanism; typically such a mechanism will involve the generation of molecules, called intermediates, which do not appear in the stoichiometric equation.

140

Rates of reaction

try:

For example, the decomposition of ozone into oxygen has the stoichiome203 —> ‘302

and it is thought that this overall process has a mechanism involving the fol-

lowing three elementary steps involving an oxygen atom as an intermediate: b;

“+

0) +0

O2 +0 — 0;

O + 03

—>

20.

A great deal of effort has been put into determining the mechanisms of

chemical reactions, 1.e. identifying the intermediates and the contributing elementary reactions. Determining a reaction mechanism is by no means a simple task and usually requires the application of many techniques, such as a study of how the rate of the reaction varies with the concentrations of the species involved and the detection of intermediates.

Rate laws for elementary and complex reactions As an elementary reaction takes place as written we can write down the rate law directly from the chemical equation. For example: OH™

+ CH3Br —>

CH30H

+ Br—

rate = k,[OH™ ][CH3Br]

Cl + 03 —

ClO + O02

rate = kp[Cl][O3]

H + Br2 —>

HBr+ Br

rate = k,[H]({Bro].

In contrast, for a complex reaction there is no way that we can write down

the rate law just by looking at the stoichiometric equation; in such cases the rate law has to be determined by experiment. A good example is the reaction between H2 and Br2 in the gas phase

H2 + Br2 —> 2HBr which has the experimental rate law: ‘

rate of formation of HBr =

ka{H2]{Bro]}°/? [Bro] + k.[HBr]

which is, to say the least, far from obvious. Indeed, the observation of such a complex rate law is good evidence for the reaction not being elementary. However, the opposite is not necessarily true: some reactions have simple experimental rate laws but turn out to have complex mechanisms! For example the gas-phase reaction between H) and Ip

H2 + Iz —>

2HI

is found to have the rate law

rate of loss of H2 = k¢[H2] [I].

9.6

Intermediates and the rate-determining step

141

Despite the simplicity of this rate law it is thought that the mechanism for the reaction may involve the intermediate IH» in the following steps (although

there are certainly other possible mechanisms)

I+

In —

2]

21

Ih

—

H2 —>

IH?

I+ IH. —>

9.6

2HI.

Intermediates and the rate-determining step

We mentioned on p. 139 that complex reactions often involve the formation of species, called intermediates, which are neither reactants nor products. The nature and properties of these intermediates often play a crucial role in the reaction, and as a result you will find that a lot of attention is focused on them.

Let us take as an example the reaction of the nucleophile OH~

with the

acyl chloride CH3COCI (discussed in Section 7.6 on p. 110). The reaction is shown in Fig. 9.9 and proceeds in two steps via the formation of a tetrahedral

intermediate, I.

7 OH

©

+

H3C~

C

step 1

Cl

—

HO

H3C~

ew

7

Ze I

(o)

step 2

—

~Cl

7

H3C~

Cc

}

OH

+

Cl

Fig. 9.9 The reaction between OH and CH3COCI proceeds in two steps. Step (1) involves nucleophilic attack on the carbonyl carbon to form a tetrahedral intermediate (I); in step (2) this intermediate collapses expelling CI~ and re-forming the carbonyl group.

It is very important not to confuse intermediates with transition states (introduced on p. 134). A transition state only has a fleeting existence and is simply an arrangement of the atoms through which the reaction must pass in order to reach the products; a transition state is located at a maximum in the

energy profile (see Fig. 9.4 on p. 134).

In contrast, an intermediate is as much a real molecule as any other — we

can probe its structure using spectroscopic and physical techniques, and indeed we may even be able to isolate it. Admittedly, it is often the case that these intermediates are very reactive and rather short lived, so studying them can be

difficult, but they do not have the fleeting existence of a Intermediates — like product and reactant molecules in the energy profile of the reaction; this is in contrast to are found at maxima. These points are illustrated in Fig. energy profile for the reaction between OH™

transition state. — are found at minima transition states which 9.10 which shows the

and CH3COCI.

The first energy barrier in this reaction is CH3COCI) and the intermediate, I; at the top transition state in which presumably the C—O the bond between the OH™ and the carbonyl

between the reactants (OH™ + of the barrier we have the first z bond is partially broken and carbon is partially made. The

activation energy for this first step is E,,;. The second barrier in the reaction is

between the intermediate and the products, and proceeds via the second transition state in which we imagine that the C—O bond is partially re-formed and the C-Cl bond is partially broken.

Rates of reaction

142

transition

>

energy

transition state 1

HO. hy

+c?

aN He07

i

cI products

reactants

———_ reaction coordinate Fig. 9.10 Energy profile for the reaction shown in Fig. 9.9. The reactants, products and intermediate all occur at energy minima, whereas the two transition states occur at maxima. The activation energy for the first step, E, 4, is shown as being much greater than that for the second, E, 9; this means that the first step is the rate-determining step.

The rate-determining step In Fig. 9.10 the activation energy for step (2) is shown as being considerably less than that for step (1). What this means is that, all other things being equal,

the rate of step (2) is much greater than that of step (1). As a consequence, the moment a molecule of the intermediate is formed in step (1) it almost immediately reacts in step (2) to give the products. The rate at which the products are formed is thus determined only by the rate of step (1), which is therefore described as the rate determining step. Assuming that step (1) is an elementary reaction we can write its rate as: rate of step (1) = ky[(CH3COCI][OH™J. It follows that as step (1) is the rate-determining step, the rate of formation of the products is the same as the rate of step (1): rate of formation of the products = k;[(CH3COCI][OH 7 ].

We see that although a two-step mechanism is involved, the rate law is rather simple.

It is important to be careful not to fall into the mistake of describing this

kind of reaction by saying that ‘the first step is slower than the second; so the former is rate-determining’. What is wrong with this is that during the reaction,

step (2) is in fact proceeding at the same rate as step (1). If the concentrations of the reactants and the intermediate were equal it would undoubtedly be the case that the rate of step (2) would be greater than

that of step (1). However, the concentrations are not equal — far from it. We expect to find that the concentration of the intermediate will be very low because it is whisked away to products as quickly as it is formed. No matter how low the activation energy for step (2) becomes, this reaction cannot take place until

9.7

Reversible reactions

143

step (1) produces some of the intermediate; as a consequence, the rate of step (2) cannot be greater than that of step (1), and in fact they are equal.

9.7

Reversible reactions

So far we have ignored the possibility that a reaction can go backwards as well as forwards, i.e. that reactions are reversible. If a reaction has a position

of equilibrium which favours the products very strongly then to a very good

approximation we can ignore the reverse reaction, but if the position of equi-

librium is more balanced between reactants and products we must consider the reverse reaction. Like the forward reaction, the reverse (or back) reaction has an activation

energy as is illustrated in the energy profiles shown in Fig. 9.11. The activation energy for the forward reaction, Ef, is the energy difference between the transition state and the reactants. For the reverse reaction, which takes us from products back to reactants, the activation energy, E,,,, is the energy difference between the transition state and the products. The profile of Fig. 9.11 (a) is for an exothermic reaction, i.e. one in which

the products are lower in energy than the reactants; it follows that the activation energy of the reverse reaction must be greater than that of the forward reaction. In contrast, for an endothermic reaction, shown in Fig. 9.11 (b), it is the forward reaction which has the greater activation energy.

From the diagram it is clear that the energy difference between the products

and reactants, AE,

is related to the activation energies in the following way: AE

=

Eat

_

Ear.

(9.3)

The energy difference is not quite the same thing as A,H°

for a reaction, but it

is closely related to it.

Inspection of Fig. 9.11 (b) shows that for an endothermic reaction the activation energy (of the forward step) cannot be less than AE, i.e. the activation energy is greater than the endothermicity. For an exothermic reaction, Fig. 9.11 (a), there is no particular relationship between the activation energy of the forward reaction and AE. (b) endothermic

energy

energy

(a) exothermic

A Eat

products ™

products —_—_—_

reaction coordinate

reactants

AE |

————_

reaction coordinate

Fig. 9.11 Energy profiles for (a) an exothermic reaction and (b) an endothermic reaction. In each case the energy difference between the reactants and products, AE, is equal to the difference in the activation energies of the forward (Eq») and reverse (Ea,r) reactions.

144

Rates of reaction

Relation to the equilibrium constant Let us suppose that we have a reversible reaction between A and B and Q:

ke

A+B

=

to give P

P+Q.

ky

We will also suppose that the forwatd and reverse reactions are elementary (with rate constants kp and k,, respectively) so that, as described on p. 140, we can write the rates of the two reactions as: rate of forward reaction = ks[A][B] rate of reverse reaction = k,[P][Q].

In Section 8.5 on p. 130 we argued that at equilibrium the rates of the forward and reverse reactions are equal. So, we can write: k[A]eq[Bleq

= k-[Pleq [Qleg

where we have added the subscript ‘eq’ to remind ourselves that this relation-

ship is only true when the concentrations are at their equilibrium values. Some rearrangement of this equation gives:

kt (PleqlQleg kr

[A]eqlBleq

We recognize the quantity on the right-hand side as the equilibrium constant,

Kegq, and so see that the ratio of the rate constants for the forward and reverse

reactions is equal to the equilibrium constant: Keg

=

T-.

(9.4)

We have already seen in Section 9.4 on p. 137 that rate constants can be ex-

pressed in terms of an A factor and activation energy using the Arrhenius equation, Eq. 9.2. If we do this for the forward and reverse reactions we have: kp = Af exp (

-E ae)

k, = A,exp (

—-E a)

where Af and A, are the A factors for the forward and reverse reactions, re-

spectively. Using these expressions in Eq. 9.4 we have: Ag exp (=e) Keg

=

_E

Ar exp ( a) _

Af

= — exp Ay

—(Ea

— Ear)

RT

At (> = — exp | —— Ar RT

where, to obtain the last line, we have used Eq. 9.3.

9.8

Pre-equilibrium

145

What the final line tells us is that the equilibrium constant varies with tem-

perature in a way determined by the value of AE, the energy change for the reaction.

If AE

is positive (i.e. an endothermic reaction), an increase in the

temperature results in an increase in the equilibrium constant. In contrast, for

an exothermic reaction which has a negative AE,

increasing the temperature

reduces the equilibrium constant. If we identify AE with A,H° these conclusions are exactly the same ones we came to in Section 8.4 on p. 122, albeit using a very different approach.

9.8

Pre-equilibrium

Look again at the energy profile for the CH3COCI

+ OH™

reaction (Fig. 9.10

on p. 142), and consider the ‘choices’ which are open to the intermediate, I. It can either go on to products, which is what we assumed would happen, or it could take the reverse of step (1) and go back to reactants. However, as the

profile is drawn the activation energy for I going back to reactants is larger than for it going on to products; we therefore expect that the latter will be the dominant process as it will have a larger rate constant. With hindsight you can see that it was no accident that the energy profile was drawn in this way! Figure 9.12 shows two different energy profiles for a two-step reaction. Profile (a) is just like that in Fig. 9.10; the dominant process for the interme-

diate is for it to go on to products and, as we have seen, this leads to step (1) being the rate-determining step. In profile (b) the activation energy for the intermediate returning to reactants is lower than for it going to products, and this

leads to quite a different result.

In the case of profile (b), once an intermediate is formed its most likely fate is to return to reactants in the reverse of step (1), which we will call step (—1).

The slower conversion from the intermediate to products via step (2) does take place but only a small fraction of the intermediates take this route.

(a) B

4

(b) z oa) D

i dominant _—_—_—_

dominant —_

3

3

Cc

P

P

——_—_—_

—-

reaction coordinate

reaction coordinate Fig. 9.12 Alternative energy profiles for a two-step reaction.

tion energy open to the intermediate I is to go to the intermediate to return to reactants, R, by the in which the first step is rate-determining; profile the text. The dominant fate of the intermediate, I,

In (a) the pathway with the lowest activa-

products, P.-In (b), the lowest energy pathway is for reverse of the first step. Profile (a) leads to kinetics (b) leads to pre-equilibrium kinetics, as described in is indicated by the arrow.

146

Rates of reaction

The picture of what is happening is therefore this: the reactants and the

intermediate are rapidly interconverting via steps (1) and (—1), with a small,

slow, ‘bleed off’ of some of the intermediate to give products via step (2). Un-

der these circumstances we are justified in assuming that the reactants and the

intermediate are in equilibrium; even though some of the intermediate goes to

form products, the equilibrium between reactants and intermediates is quickly

re-established. Step (2) is the rate-linfiting step as its rate constant controls the

rate of formation of the product. This idea that the intermediate (or intermediates) are in equilibrium with the reactants is called the pre-equilibrium hypothesis. The ‘pre-’ comes about

because this equilibrium precedes the rate-determining step. This kind of situation is quite commonly encountered, particularly if the pre-equilibrium steps involve protonation and deprotonation; let us see an example of how this works out.

Example: oxidation of methanoic acid with bromine In aqueous solution, methanoic (formic) acid is oxidized to CO2

cording

to the stoichiometric equation:

by Br

ac-

HCOOH + Br2 + 2H20 —> CO, + 2Br~ + 2H307+. This reaction has been investigated experimentally and it is found that the rate of the reaction is sensitive to the concentration of H3O* in the solution (this can be varied by adding a strong acid, such as HCl). The rate law is found to be: k[Br2][HCOOH]

rate of consumption of Brz =

[H307]

(9.5)

This rate law tells us that the rate goes down as the concentration of H30+

goes up, i.e. the reaction is inhibited by H30°. This gives us a clue as to what might be happening in this reaction: suppose that the bromine actually oxidizes

the anion HCOO™

rather than the methanoic acid itself; this anion would have

to be formed by the usual dissociation of the methanoic acid:

HCOOH + H20 = HCOO™

+ H30°%.

Increasing the amount of H30* (for example by adding a strong acid) would shift this equilibrium to the left (see p. 126) and so decrease the amount of

HCOO™

present; this would then explain why the rate decreases as the con-

centration of H3O* increases.

With this in mind we propose the following mechanism: ks

HCOOH + H20 — HCOO™ +H307 k 4

HCOO™

+ Br sy products

We have numbered the steps (3),

steps (3) and (—3) step (4).

(—3) and (4) to avoid confusion with steps (1)

and (2) in the reaction in Fig. 9.9 on p. 141.

9.8

Pre-equilibrium

147

The first line is simply the acid dissociation equilibrium. We have written

the rate constants of the forward and reverse reactions as k3 and k_3, respectively, but recall from the discussion on p. 144 that the equilibrium constant is the ratio of these two rate constants:

Ka

=i

(9.6)

If we assume that pre-equilibrium applies, then we can find an expression

for [HCOO7] using the definition of the equilibrium constant, Ka: K,

=>

[H30* ][HCOO7] [HCOOH]

This can be rearranged to give K,

[HC

[HCoo~} = SsCOOH] [H307]

The rate of consumption of bromine is just the rate of step (4), so rate of consumption of Br2 = k4[HCOO™

[Bro]

_ kaKal[HCOOH][Bra] 7

[H30*]

The rate law we have derived is therefore

rate of consumption of Br2 =

kerp[ HCOOH] [Br2]

[H307]

where Keg; iS

and on the last line we have used Eq. 9.6.

The rate law we have predicted has the same form as the experimental

rate law, Eq. 9.5, which at least means that our mechanism is consistent with

the experimental observations and that the pre-equilibrium assumption is valid

for this mechanism.

Finally, it shows us that the experimental rate constant

is in fact a composite of three rate constants, or — looked at another way — a composite of a rate constant and an equilibrium constant. When can we apply the pre-equilibrium assumption? For the pre-equilibrium assumption to be valid the rate constants have to be such that an intermediate, once formed, is much more likely to return to where

it came from than to go on to react further. In other words, the further reactions of the intermediate must be slow compared to the intermediate returning to the species from which it was formed. A common situation in which these conditions hold is when the intermediate is formed by protonating or deprotonating one of the reactants. Such proton transfers often have rather large rate constants — they are sometimes described as being ‘facile’ or ‘easy’ processes.

148

Rates of reaction

9.9

The apparent activation energy

For any reaction — be it an elementary reaction or one with a complex mechanism — we can always determine the activation energy by measuring how the

rate constant varies with temperature and then fitting the data to the Arrhenius equation in the way described on p. 138 and illustrated in Fig. 9.8. If the reaction 1s a complex one proceeding via a number of elementary steps, the question is what is the relationship between this measured activation energy

(we will call this the apparent activation energy) and the activation energies of

the elementary steps? We will use the two reactions we have been discussing in this chapter to illustrate this relationship and this will lead us to a rather neat general conclusion about the size of the apparent activation energy.

The reaction between CH3COCI and OH™ (Fig. 9.9 on p. 141) proceeds by

a two-step mechanism:

CH3COCI + OH “4 I 1-2; CH;COOH +CI-

step (1) step (2).

We argued that if the first step is rate-limiting the overall rate just depends on

the rate constant for step (1):

rate of formation of the products = ky [CH3COCI][OH7].

We can write the rate constant k; using the Arrhenius equation (Eq. 9.2 on

p. 137) as:

k,; 1

= A) 1 ex p(

—Eq)

RT — ) },

Therefore the apparent activation energy for the overall reaction is exactly the same as the activation energy for step (1), the rate-limiting step.

Identifying the activation energy for the oxidation of methanoic acid is a little more complicated; let us remind ourselves of the reaction scheme: ky

HCOOH + H20 = HCOO™ + H30* k_3

HCOO™

_

k

+ Br. —>

products

steps (3) and (—3) step (4).

We found that by applying the pre-equilibrium assumption the overall rate law

was:

rate of consumption of Brz = where

kerp[HCOOH][Br]

[H30*]

9.9

The apparent activation energy

149

We now write each rate constant in the expression for kerr using the Arrhenius law:

A4 exp (=H) kett =

=

A3 exp (ae

A_3 exp (=H) A4A3

A_-3

exp

(Ss

+

E43

_

E,,-3)

RT

.

From this we can identify the apparent activation energy as the energy term in

the exponent:

Ea apparent = =

Ea4

+

Ea3

_

Ea,-3

9.7

Ea,4 + AE3

O7)

where on the last line we have used the relationship between the energy change for a reversible reaction and the difference in activation energies between the

forward and reverse reactions: AE = E43 — Ea,—3 (Eq. 9.3 on p. 143).

We see in the case of this mechanism that the apparent activation energy

depends on the activation energies of all three steps or, alternatively, on the energy change of the reversible reaction and the activation energy of the final step. The general result In fact, there is a simple result which describes both reaction schemes. It is that

the apparent activation energy for a reaction is the energy difference between

energy

energy

the reactants and the highest energy transition state on the reaction pathway: this is illustrated in Fig. 9.13. Profile (a) is appropriate for the reaction between CH3COCi and OH™ in which the first step is rate-determining and so the highest energy transition state

—————“

——_p-

reaction coordinate

reaction coordinate Fig. 9.13 Two different energy

profiles showing

how the apparent

activation energy

is equal to the

energy separation between the reactants and the highest energy transition state along the reaction pathway. Profile (a) is for the reaction between CH3COCI and OH™; the first step is rate-determining and so has the highest activation energy. The apparent activation energy is therefore equal to the activation energy of the first step. Profile (b) is for the reaction between HCOOH and Bro; the second

transition state is the highest energy point and so the apparent activation energy depends on the activation energies of all of the reactions, as described in the text.

150

Rates of reaction

on the reaction profile is the first transition state we encounter.

activation energy is simply the activation energy of the first step.

The apparent

Profile (b) is for a reaction in which the first step is reversible, such as the

reaction between HCOOH and Brp which we have been discussing. The second

transition state, between the intermediate and the products, is now the highest

energy point on the pathway and so this determines the apparent activation

energy. As we have discussed, this activation energy can either be expressed in terms of the activation energies of all three reactions or the energy change of the first reaction and the activation energy of the second (Eq. 9.7).

9.10

Looking ahead

We mentioned at the start of this chapter that a knowledge of the rates of reactions can be helpful in teasing out the mechanisms of complex reactions. The oxidation of methanoic acid is a good example of this — we saw that the rather

unusual rate law, in which H3O0* was seen to inhibit the reaction, suggested a

mechanism which we went on to show was consistent with the experimental

rate law.

In the coming chapters we will see a great deal more of how a study of kinetics helps us to unravel the mechanism. For example, consider the follow-

ing two nucleophilic substitution reactions and their experimentally determined rate laws:

CH3Br+ Nu”

—>

CH3Nu + Br-

(CH3)3CBr + Nu~ —> (CH3)3CNu + Br

rate = k[CH3Br][Nu]

rate = k’[(CH3)3CBr].

Note that the reaction involving bromomethane is first order in both the nucleophile and the alkyl halide, and hence second order overall. In contrast, for the 2-bromo-2-methylpropane (t-butyl bromide) the concentration of the nu-

cleophile does not appear in the rate law, making it first order overall. How can

this be? We will see in Chapter 11 how changing the alkyl group from methyl to t-butyl causes a change in mechanism and hence in the rate law. However, before we can understand that we must look at a further electronic effect — delocalization and conjugation.

10

Bonding in extended systems — conjugation

In Chapter 6 we introduced hybrid atomic orbitals and used these as the basis for a localized description of bonding; such an approach is perfectly adequate

for many molecules, especially those commonly encountered in organic chemistry. We then saw in Chapter 7 how we could use a knowledge of orbitals to help us to understand and rationalize reactions. In the following chapters we want to move on to some reactions which involve molecules and intermediates whose bonding cannot be described ade-

quately using only the localized approach of Chapter 6. The kind of molecules

we are talking about typically have extended wz systems and are often charged; we will see that a proper description of the bonding in such molecules needs the delocalized MO approach for parts, but not usually all, of the molecule.

For example, let us consider how to describe the bonding in propene and

benzene (Fig. 10.1). For propene we choose sp? hybridization for C), and sp” hybridization for the other two carbons. The overlap of these hybrids with one another or with hydrogen 1s AOs gives us the C-C and C-H o bonds, and the

mz bond is formed by the overlap of out-of-plane 2p orbitals on C2 and C3. For

propene, this localized description is entirely adequate. For benzene we choose all of the carbons to be sp* hybridized and once

again form C—C and C-H o bonds by overlapping these HAOs with one another and with the hydrogen 1s AOs. The six out-of-plane 2p orbitals then overlap in three pairs to form three mz bonds, thus giving alternating single and double bonds round the ring. However, the problem with this localized description is that there is much

H3C~

“a

5 SCH,

physical and chemical evidence that all the C-C bonds in benzene are the same

(for example, they are all the same length); a structure in which there are alternating single and double bonds is simply not consistent with these observations. Benzene is therefore an example of where a delocalized description is required.

You may have come across the idea of using resonance structures to explain the delocalized nature of the bonding in benzene. The idea is illustrated in Fig. 10.1 where two different structures for benzene are shown which only

differ in the placement of the double bonds. On their own, both structures are an inadequate representation of the bonding in benzene, but the two taken together convey the crucial point that there is 7 bonding between all the adjacent carbons. In a sense, the ‘real’ structure of benzene lies in between these two, and this is what the structure at the bottom of Fig. 10.1 tries to convey — the

circle indicating that the 7 bonds are delocalized round the ring. It is tempting to think that the molecule flips between these resonance structures, but this is a mistaken view. These structures are simply our attempts to

Fig. 10.1 The bonding in propene can be described adequately using 2c-2e bonds, but benzene requires a delocalized

approach for the x system. The two resonance structures for benzene, connected by a double headed arrow, are an attempt to describe this delocalized

bonding using structures with localized bonds. The structure at the bottom, in which a circle is drawn in place of the

separate 7 bonds, is another way of representing the delocalized bonding in benzene.

152

Bonding in extended systems — conjugation

MOs of benzene; positive and negative Fig. 10.2 Surface plots of the three highest energy occupied parts of the wavefunction are indicated by different shading of the grid lines. The skeleton of the benzene molecule is also indicated. These three MOs are clearly formed from the overlap of the outof-plane 2p orbitals; the lowest energy MO, 17, is reminiscent of the ‘doughnut’ picture often used to explain the delocalized x bonding in benzene.

make a localized description of the bonding in a molecule which in fact has

delocalized bonding. No one of the structures is an adequate representation of the actual bonding, but taken together they convey something closer to the truth.

A useful analogy here is that of an mule, which we get by crossing a horse

with a donkey. To describe an mule as a horse or a donkey would be inaccurate and it certainly does not interconvert rapidly between the two! Rather we need to recognize that although an mule has parts that are reminiscent of a horse and parts that are reminiscent of a donkey, it is something altogether different.

The MO picture of benzene naturally takes a delocalized view of the bonding, and the three highest energy occupied MOs shown in Fig. 10.2 illustrate this very well. It is clear from looking at these MOs that they are formed from

the overlap of 2p orbitals which point out of the plane of the molecule, and indeed you may recognize the 1a MO as being like the ‘doughnut’ picture often given to explain the equivalence of the C-C bonds in benzene. However, this

doughnut is just one of the six MOs which are formed from the overlap of the six out of plane 2p orbitals; only three of the MOs are occupied, and these are

the ones shown in Fig. 10.2. It is not really necessary to use the delocalized MO approach to describe all of the bonding in benzene. By using sp* hybrids on the carbons we can generate a o framework of 2c-2e C-H and C-C bonds, just as we described

above. The MO approach is only needed to treat the six out of plane 2p orbitals. This way of descrtbing benzene is typical of the approach we will adopt.

The majority of the bonding in a molecule can usually be described using 2c-2e

bonds to give the o framework. This leaves a few orbitals, typically pointing out of the plane of the o framework, whose interaction we need to treat using

the MO approach. What we will see in the next section is that it is quite easy to construct delocalized 2 MOs which are formed from 2p orbitals arranged in a row; such an

arrangement is surprisingly common in molecules and so we will find imme-

diate use for these MQOs in describing aspects of structure and reactivity. We will start with four p orbitals in a row to introduce the idea and then reduce the number to three; this might seem a bit illogical, but it turns out that it is easier

to see what is going on if we start with four orbitals.

10.1

10.1.

Four p orbitals in a row

153

Four p orbitals in a row

A good example of what we mean by a ‘row of p orbitals’ is the case of butadiene, shown in Fig. 10.3. We can describe the bonding in this molecule by

H

making all of the carbons sp* hybridized, and then using these orbitals to form

H»C

2c-2e bonds with the hydrogens, and carbon-carbon o bonds between the adjacent carbons. There are 22 valence electrons in butadiene, four from each

carbon and one from each hydrogen.

ber that in Section 5.4 on p. 68 we described how the number of MOs is equal to the number of AOs which are being combined).

be a linear combination of the four AOs: MO

These four MOs will each

= c) AQ; + c2AQO2 + c3A03 + cq4AO4

where AO, is the AO on atom 1, and c, is the coefficient for this AO and so on. These coefficients are a measure of the contribution that each AO makes to the MO. It is relatively easy to compute the energies of the MOs and the cor-

responding coefficients; the results are presented in cartoon form in Fig. 10.4.

energy

4n

1x

{ ‘in a line’. The coefficient Fig. 10.4 Cartoons of the four x MOs resulting from four 2p AOs overlapping of the coefficients are some that note AO; the of size the by indicated is AO each of n) (or contributio

lowest in-energy and has no nodes negative so the sign of the AO has been inverted. MO 1m is the atoms 2 and 3. As the energy rises between node one has and lowest between the atoms; 27 is next

. The orbital coefficients are to MOs 37 and 4x the number of nodes increases to 2 and 3, respectively the right; for 1 there is one on shown as molecule, the given by a sine wave which can be drawn over half sine wave, for 27 there are two and so on.

ee H

butadiene

The o framework uses up 18 of these

electrons, leaving four to go into the out of plane z system which is formed from four 2p orbitals. We know that these four 2p orbitals will overlap to form four MOs (remem-

Zon

"o-®s¢°

Sy

OHO60C

o framework

m™ system

HoH Fig. 10.3 At the top is shown the conventional representation of butadiene, with two C—C double bonds separated by a C-C single bond. If the carbons are

sp@ hybridized the bonding can be

described as a o framework formed from the overlap of these hybrids with one another and with the hydrogen 1s AOs, together with a delocalized x system formed from the overlap of the out-of-plane 2p AOs. These orbitals are an example of four p orbitals in a row.

154

Bonding in extended systems — conjugation

The o framework lies in a nodal plane for each MO; this is why the MOs are _ designated 7. First look at the energies of the MOs: there are two MOs lower in energy than the AOs and two higher.- The first two are therefore bonding MOs and the latter two are anti-bonding.

The coefficients of the AOs fall into a simple pattern as the MOs go up in energy. In the lowest energy MO, 17, all of the coefficients are positive; there is therefore constructive overlap betweeh all of the adjacent orbitals and it is therefore not surprising that this MO is the most strongly bonding.

In 27 there is a nodal plane between atoms 2 and 3; there is thus constructive interference between the AOs on atoms | and 2, and between those on atoms 3 and 4, but destructive interference between atoms 2 and 3. Since there are two constructive interactions but only one destructive, the orbital is overall bonding, but not as strongly as Iz. MO 3z has two nodal planes (between atoms | and 2, and 3 and 4), so

there is destructive overlap between the AOs on atoms | and 2, and 3 and 4. There is constructive overlap between the AOs on atoms 2 and 3, but this time

(in contrast to 27) the orbital coefficients are such that the orbital is net antibonding. Finally, 477 has a nodal plane between each adjacent atom, and so there is only destructive interference; it is therefore the most anti-bonding MO. The general pattern is that the number of nodal planes increases as the energy goes

up; this is a feature of both AOs and MOs which we have seen before. It turns out that for each MO the coefficients follow a sine curve which

can be inscribed over the molecule in a particular way. As the energy goes up the number of half sine waves increases, as is shown in the diagram. The

coefficients for the jth atom in the kth MO are given by .

sin

jkr

N+1

where N is the number of AOs which are overlapping; N = 4 in the case of

butadiene.

So, for MO 37, which has k = 3, the coefficients are:

cy = sin1x3 ( : *) = 40.95

2 ec =sin ( |

c3 = sin(3x3 ( = *) = 0.59

4 cy=sin ( =~] = +0.95

= ~0.59

which match up with the picture shown in Fig. 10.4 (to compute these you need to remember that the argument of the sine is in radians, not degrees). Butadiene

In butadiene we have four electrons to place in the 7 system;

we therefore

put two (spin paired) in 1 and two in 27. All of the electrons are therefore accommodated in bonding MOs.

MO Im gives rise to m bonding across the whole molecule so, In contrast to the simple picture shown in Fig. 10.3, there is 2 bonding between C2 and C3. In fact, because in I the coefficients on C> and C3 are the greatest (see

10.1

Four p orbitals in a row

155

Fig. 10.4), this MO contributes more to the bonding between C2 and C3 than it does to the bonding between C, and C2 or C3 and C4. MO 27 has a node between C2 and C3 and so gives rise to an anti-bonding

interaction between these two atoms. However, because of the smaller orbital

coefficients on these atoms, the anti-bonding interaction does not outweigh the bonding interaction due to 177. So, overall, the occupation of MOs Iz and 27 leads to some z bonding between C2 and C3.

MO 2z also gives rise to a bonding interaction between C; and C2, and

between C3 and C4. However, the contributions from MOs

1x and 27 do not

add up to the same amount of 7 bonding as is present in the simple 2c-2e 2

bond in ethene. So in butadiene the degree of 7 bonding between C, and C2 and between C3 and Cy is less than in ethene.

\

The overall picture for butadiene is of 2 bonding across all four carbons,

HC a

in butadiene is shorter than the C-C single bond in propene, but not as short Similarly, the nominal double bond in butadiene

1.349

7 bonding between C2 and C3, and a weakening of the z

Hoc’

bonding between C, and Co, just as we predicted from the MOs. The two a bonds which we drew in the simple structure of butadiene are described as being conjugated, which means that they form a pattern of alternating single and double bonds; the key feature of such systems is that they contain an uninterrupted chain of p orbitals lying out of the plane of the o

framework.

In conjugated systems the mz bonding is not localized between

pairs of atoms, but rather is delocalized across the whole conjugated system. A proper description of the bonding in such a molecule requires the delocalized

MO approach.

In contrast, a molecule such as CH2=CH—CH2—CH=CH1?

CHg 1.467

Vat 2 Cc Aa4

between C; and C2 is a little longer than the double bond in propene. These data point to partial

1.506

ON

but with a larger interaction between atoms 1 and 2, and 3 and 4. The bond length data give in Fig. 10.5 confirm this description. The C2—C3 bond length as the C-—C double bond.

H

{

H 3

Fig. 10.5 Experimental bond length data, in A, for the C-C bonds in propene and butadiene. The C;—Cz bond in butadiene is longer than the C—C double bond in propene, whereas the Co—-Cz bond is shorter than the C—C single bond in propene. These data provide evidence for there being partial x bonding between Co

and

C3.

is not conjugated

as the m bonds are separated by two o bonds; a localized description of the bonding is perfectly adequate for such a molecule. In summary, because the two z bonds in butadiene are conjugated the simple structure given in Fig. 10.3 does not really describe the bonding adequately. In fact, the four electrons assigned to the two z bonds in the simple structure

are occupying x MOs which are delocalized over the whole molecule and so give rise to 2 bonding between all the adjacent carbon atoms.

Propenal Propenal (also called acrolein), whose structure is shown in Fig. 10.6, is closely related to butadiene; both have two conjugated double bonds with a total of four a electrons. Just as we did in butadiene, we can model the 7 system in

propenal as four 2p orbitals in a row. The crucial difference, however, is that the four orbitals no longer have the same energy — the oxygen orbital is lower in energy than that on the carbon (see Fig. 4.34 on p. 57). The four 2p orbitals

will still give rise to four MOs, but they will not be quite the same as those shown in Fig. 10.4; the presence of one oxygen AO will alter both the energies and the orbital coefficients of the MOs. It requires a computer calculation to work out the MOs which are shown, as surface plots, in Fig. 10.7.

propenal Fig. 10.6 The structures of butadiene and propenal; to go from one to the other all we have to do is replace the CHo at position 1 in butadiene with an oxygen.

Bonding in extended systems — conjugation

156

Fig. 10.7 Surface plots of the four 7 MOs in propenal; the numbering scheme matches that used in Fig. 10.8 and that of the corresponding MOs in butadiene shown in Fig. 10.4.

Broadly speaking the four MOs are comparable with those for butadiene shown in Fig. 10.4 on p. 153. MO

Iz: is the lowest in energy and has no nodal

planes between the atoms. For propenal the coefficient of the AO from Cg is so small that it hardly shows up on this plot. MO 27 is the next highest in energy; as in butadiene it has constructive

overlap between the AOs on C3 and Cg, but in propenal the coefficient of the AO from C2 is very small so there is little constructive overlap between this AO and the one from oxygen. Finally, just as in butadiene, MOs 3m and 4x have two and three nodal planes, respectively.

Figure 10.8 shows the computed ordering of the MO energies for propenal;

4n 3x C=

p. 153. It always turns out that the lowest energy MO will be lower in energy than the lowest energy AO, and the highest energy MO

is higher in energy

than the highest energy AO; all of the MO diagrams you have seen conform to this pattern. The other two MOs lie somewhere in between, and it is not really possible to guess where they will fall. What we do know is that as the number

o— 2n 1n AOs

compare these with the corresponding MOs in butadiene shown in Fig. 10.4 on

MOs

Fig. 10.8 MO diagram for the x system in propenal. As explained in the text, the lowest energy MO (1:7) lies below the lowest energy AO and similarly the highest energy MO (4:7) lies above the highest energy AO.

of nodes in an orbital increases, so will the energy, and this is consistent with

the ordering shown in Fig. 10.8. In Section 5.6 on p. 76 we described the MOs formed from the overlap of two AQOs of unequal energies. What we found was that the two AOs do not contribute equally to a given MO, and that the AO which is closest in energy to a particular MO is the major contributor to that MO. This same idea carries forward to more complex situations, so we expect that the 12 MO in propenal will have a greater contribution from the oxygen AO than will 47; the surface plots in Fig. 10.7 bear this out. There are four electrons to accommodate in this 7 system, so the la and

27 MOs are occupied, making 27 the HOMO and 3z the LUMO. The Iz MO

contributes to bonding between C2 and the oxygen, with a smaller contribution between C2 and C3. The C2—-C3 bond length of 1.484 A, shorter than a typical

C-C single bond, confirms the presence of partial

7 bonding between these

10.2

Three p orbitals in a row

157

two atoms. MO 2z contributes only to bonding between C3 and C4, making a mz bond just as in the localized structure.

The way in which this partial double bond character between C> and C3 can be represented using localized 2c-2e structures in shown in Fig. 10.9. H

C

HecA_Pc

Cc

He *_*c~

H

B

Fig. 10.9 Resonance structures for propenal which illustrate the partial and 3; resonance structure B contributes less than structure A.

H

bonding between carbons 2

The fact that the Cp—C3 bond length is only slightly shorter than a typical C-C single bond suggests that resonance structure B only makes a minor contribution. This structure also suggests that there is more electron density on the

oxygen and less on C4.

The removal of electron density from C4 is supported by the observation

that, whereas C=C bonds are not usually attacked by nucleophiles (Section 7.4 on p. 106), such attack is sometimes seen for conjugated C=C bonds. For

example, CN™ can either attack the carbonyl carbon directly (like the reactions in Section 7.3 on p. 102), or it can attack at C4, as shown in Fig. 10.10.

10.2

Three p orbitals in a row

When three p AOs overlap in a line, three MOs are formed and these can be constructed in just the same way that we did for four overlapping p orbitals; Fig. 10.11 shows the MOs in cartoon form. As before, the energy of the MOs

increases as the number of nodes increases, and the orbital coefficients are given by sine waves which can be inscribed over the molecule. The one slight difference between the overlap of three as opposed to four orbitals is that in the former case one of the MOs (277) is non-bonding (it has approximately the same energy as the AOs). That this is so can also be seen from the form of the MO; the orbital coefficient on the central atom is zero so

there is neither constructive nor destructive overlap between AOs on adjacent atoms. The end carbons are too far apart for their AOs to interact significantly.

Understanding the 7 MOs which are formed from the overlap of three p orbitals turns out to be very useful for rationalizing all sorts of observations, such as why amide bonds are flat and why the two C-C bonds in the allyl anion are of equal length. Allyl anion The allyl anion can be thought of as arising from the removal of Ht from propene, as shown in Fig.

10.12; a very strong base is needed to remove a

proton from this molecule. The bonding in the allyl anion can be described by having sp? hybridization on each carbon atom; these hybrids overlap with one another or hydrogen 1s orbitals to give a o framework. The remaining out-of-plane 2p orbitals overlap to form the three MOs pictured in Fig. 10.11.

H

4H

Fig. 10.10 In the reaction between CN— and propenal the nucleophile can also attack C4 as well as the carbonyl carbon.

Bonding in extended systems — conjugation

158

po

SM

3)

energy

ay ——tf

a eneeen ences ——

Pn

———

in

CO

1 Fig. 10.11 Cartoons of the three is drawn in the same way as Fig. can be drawn over the molecule; so on. As expected, the energies

s MOs resulting from three 2p AOs overlapping in a line; the diagram 10.4. As before, the orbital coefficients are given by sine waves which for the 17 MO there is one half sine wave, for 27 there are two and of the MOs increase as the number of nodes increases.

The (valence) electron count in the anion is four from each of the three

H |

H

He o7™ oa H

|

propene

|

H

having 27 occupied does increase the electron density on the two end carbons preferentially over the centre carbon.

oN ge

allyl

l

anion

As Iz is symmetrical about the centre, we conclude that the two C-C bonds

must be identical. Indeed, experiment bears this out and the bonds are found to be the same length. It is also interesting to compare this bond length with those

H

Fig. 10.12 The allyl anion can be formed by the action of a very strong base on propene.

1.341

Iz and two to 27.

Occupation of 12 contributes to the 7 bonding over all three atoms, whereas occupation of 27 contributes nothing to the 2 bonding. However,

H

H

the o framework and the remaining four go into the 2 system. We thus assign

two electrons to MO

H

strong base

HN

carbons, plus one from each of the five hydrogens plus one more electron for the negative charge; this gives a total of 18 electrons. Of these, 14 are used in

1.506

in propene (Fig. 10.13); we see that the bond length in the anion is intermediate between that of the C-C single and double bonds in propene. Since there are only two electrons (these in 17) which are contributing to the bonding across

three atoms we expect the m bonding to be partial, which is just what the bond length data indicate.

The other interesting thing about the ally] anion is how the electron density

differs between the carbons. MO Iz has the greatest orbital coefficient, and hence the greatest electron density, on the central carbon. However, MO 27

puts the electron density on the end carbons and none in the middle. It takes a more detailed calculation to work out which of these two wins — in fact it turns out that the end carbons have the greatest z electron density. Fig. 10.13 Comparison of the C-C bond

lengths (in A) of propene and the allyl

anion. The anion is symmetrical and has a bond length intermediate between the single and the double bond in propene.

To explain these properties of the allyl anion using localized structures, we have to draw two resonance structures, as shown in Fig. 10.14. These structures

convey the idea that the charge is delocalized and may be ‘found’ on either of the terminal carbons; similarly, the double bond may be located between Cj

10.2

Three p orbitals in a row

159

and C» or between C2 and C3. This picture is consistent with the MO approach which, as we have explained, predicts a symmetrical structure with partial 7

bonding and maximum electron density on the end carbons. Sometimes the anion is represented using a dashed line across all three atoms to indicate the partial 2 bond; such a structure is also shown in Fig. 10.14.

po CH>

HoC

—- HC”HoySc,

Ho

HHe~ SCH>

Fig. 10.14 On the left, connected by a double-headed arrow, are two resonance structures for the allyl anion. On the right is an alternative representation in which the dashed line shows the partial x bond across all three atoms. In this structure the minus signs in brackets (—) indicate the positions where negative charge can be found, as shown by the resonance structures on the left.

It is interesting to compare the two resonance structures with the form of

the HOMO. Recall that this MO, the 277, has the electron density confined to

the end carbons. This is exactly where the negative charge is located in the resonance structures. There are some parallels, therefore, between the form of

the HOMO and the charge distribution predicted by the resonance structures. Carboxylate anion

Closely related to the ally] anion is the carboxylate anion, formed by removing

Ht from the OH group of a carboxylic acid, as shown in Fig. 10.15.

R—c

p \

OH

a8

p—-c¢

p Ve

O

=—+

>

«SOR-C

2 \

O

20

R—C!

\

6 (-)

Fig. 10.15 A carboxylate anion is formed when a base removes Ht from a carboxylic acid. The 7 system in the anion is delocalized and can be described using two resonance structures, or represented using a dashed line to indicate a partial bond.

The resulting anion can be described in very similar terms to those used for the allyl anion, the only difference being that instead of the 7 system being

formed from three carbon 2p orbitals it is formed from one on carbon and two

on oxygen. Surface plots of the three 7 MOs are shown in Fig. 10.16 — they are very reminiscent of the cartoons shown in Fig. 10.11 on p. 158.

Fig. 10.16 Surface plots of the three 7 MOs of the methanoate ion, HCOO-. The molecule is viewed sideways on with the two oxygens coming toward and the hydrogen going away from us. Note the similarity between these MOs and the cartoons shown in Fig. 10.11 on p. 158. MO 2z is the HOMO

and 37 is the LUMO.

Of these MOs, only the 1m and 27 are occupied, so the conclusions about

the carboxylate are much the same as for the ally] anion, i.e. there is partial m bonding across all three atoms, the negative charge 1s greatest on the two

Bonding in extended systems — conjugation

160

oxygens and the two C—O bonds are equivalent. Experimental data confirm that these two C-O bonds have the same bond length of 1.242 A. This value is intermediate between a typical C=O bond length of 1.202 A and a typical

C-OH bond length of 1.343 A, confirming that there is partial 7 bonding across all three atoms.

As is shown in Fig. 10.15, these features of the bonding in the carboxylate ion can be represented either using resonance structures, or a dashed line to represent a partial bond.

Amides Studies of the structures of amides using experimental techniques such as Xray diffraction show us that the bonds to the carbonyl carbon, the nitrogen and

the two hydrogens attached to the nitrogen all lie in the same plane, as shown in Fig. 10.17.

o

oy

:

eee sp?-1s

sp?

\

Hyvol

Vere

ZH Nw

sts

L

Fig. 10.17 Ail of the bonds within the shaded box of this amide structure are found to lie in the same plane. This being the case, the a framework of methanamide is best described as being formed from the overlap of sp* hybrids on oxygen, carbon and nitrogen. Two lone pairs occupy the remaining two

sp hybrids on oxygen.

Given the planarity of the amide, to describe the bonding we should choose sp” hybrids for both the carbonyl carbon and the nitrogen. As we discussed on p. 92 it does not matter too much whether we choose the oxygen to be sp or sp? hybridized, so we will choose sp’. With this hybridization scheme the a framework of methanamide is straightforward to form and is shown Fig. 10.17.

The planarity of the amide group means that the remaining three p orbitals

(one each on carbon, nitrogen and oxygen) are all perpendicular to the plane

and so in the correct geometry to overlap with one another to form 2 MOs. The z system can be modelled as three p orbitals in a row but, unlike the ally] anion, the AOs do not have the same energy. From Fig. 4.34 on p. 57 we expect that the AO from oxygen will be lowest in energy, next will nitrogen and the highest will be the AO from carbon. Figure 10.18 shows surface plots of these three 2 MOs; trons in the 7 system, so these occupy MOs 17 and 27. The (17r) is bonding across all three atoms. At the level plotted,

come the AO from

there are four eleclowest energy MO MO 27 shows vir-

tually no contribution visible from the carbon AO and so this MO contributes little to the bonding. between the atoms.

As there geometry we arrangement, lone pair not

Finally, as in the allyl anion, 37 has two nodal planes

is experimental evidence that amides invariably adopt this planar conclude that this must have the lowest energy. The alternative in which the nitrogen is pyramidal and sp? hybridized with the involved in the 2 system must therefore be higher in energy. The

10.2

Three p orbitals in a row

SOA No

A+ t

SSS 7

yy ,

er


Lee

aS

foe

_— RNH} ROH + H+ —> ROH;. As we saw on p. 106, in these reactions the HOMO is a lone pair and the LUMO is the 1s orbital on the H*. Amines turn out to be much more basic than alcohols, meaning that amines are more ready to pick up a proton; an explanation for this in terms of orbitals is as follows. In these reactions, the HOMO

is a lone pair on nitrogen or oxygen and

these orbitals clearly lie lower in energy than the LUMO of the Ht. However, the oxygen lone pair is lower in energy than the nitrogen lone pair, and so the energy separation between the HOMO and LUMO is greatest for oxygen. There is thus a poorer interaction with the lone pair on oxygen compared to that on nitrogen, resulting in the alcohol being the weaker base. Given that this is the case, it is at first sight surprising that when an amide acts as a base it is the carbonyl oxygen which is protonated first, not the nitrogen (Fig. 10.25). In other words, the carbonyl oxygen is more basic than the nitrogen. ‘0 SN

‘0@_H ”

Fig. 10.25 In an amide the carbonyl oxygen is more basic than the nitrogen.

To understand what is going on here we first need to identify the HOMO

of

the amide. There are two candidates: either the lone pair on the nitrogen, or one of the lone pairs on the oxygen. As we discussed before, the carbonyl oxygen can be considered as sp” lone pairs; these hybrids involved in the z system. From what we know would expect the oxygen

hybridized and two of these hybrids are occupied by lie in the plane of the molecule and therefore are not

about the energies of AOs (see Fig. 4.34 on p. 57) we lone pair to be lower in energy than that on nitrogen,

so the latter would form the HOMO. However, as we have seen the interaction

of the nitrogen lone pair with the carbonyl z system results in a lowering of the

energy of the lone pair as it moves into the 27 MO (see Fig. 10.19 on p. 161). In the case of the amide, the nitrogen lone pair is so lowered in energy that it comes below the oxygen lone pairs thus making the latter the HOMO. So the best energy match to the LUMO of the proton is the lone pair orbital on the

oxygen.

10.3

Chemical consequences — reactions of carbonyl compounds

165

We can also formulate an explanation of this effect using resonance struc-

tures.

In Fig. 10.21 on p. 162 it is illustrated how the lone pair can become

involved in the formation of a C-N z bond. This decreases the ‘availability’ of the nitrogen lone pair, thus reducing the basicity of the nitrogen.

Amides and acy! chlorides

As we have seen in Section 7.6 on p. 110 acyl chlorides react very rapidly with

nucleophiles, usually leading to subsequent elimination of CI~, whereas, as we have already noted, amides are rather unreactive. The reaction, or lack of it,

with water (shown in Fig. 10.26) offers a clear demonstration of this difference. Hd

“

0

VIE

R~

No

RE

coal

H,0 2

/

O°

R~ Cc No

fast

O

I

H20

Cw R

\

——_—s

—_—>—s_—

fo) |

R~ Cc SoH

+

ce’

no reaction

NHs

Fig. 10.26 Acyl chlorides react rapidly with water as a nucleophile, ultimately generating a carboxylic acid and chloride ions; amides are unreactive to water.

An explanation you will often find given for the high reactivity of the acyl chloride is that the chlorine is electron-withdrawing and so this increases the partial positive charge on the carbonyl carbon, making it more reactive towards

nucleophiles. The problem with this argument is that nitrogen is also electronwithdrawing; in fact chlorine and nitrogen have about the same electronegativ-

ity, so if the presence of an electron-withdrawing chlorine substituent increases

the reactivity of the carbonyl, a nitrogen substituent should do the same — which

plainly it does not. To sort out what is going on here we have to realize that the presence of the substituent X in RCOX has two effects. The first is that the electronwithdrawing nature of X increases the positive charge on the carbonyl carbon

thus increasing its reactivity toward nucleophiles; this is called the inductive effect. The second is the conjugative effect described on p. 163; in this the delocalization of a lone pair from X into the carbonyl 2 system decreases the

reactivity of the carbonyl towards nucleophiles by raising the energy of the 2*

LUMO.

As nitrogen and chlorine have about the same electronegativity, and hence presumably the same inductive effect, we must look to the conjugative effect to

explain the difference in reactivity between the acyl chloride and the amide. It

must be that the conjugative effect (which decreases reactivity) is much greater for the amide than for the acyl chloride.

The explanation for this is that the orbital involved in forming the delocal-

ized system is a 3p in chlorine and a 2p in nitrogen.

The 3p is much larger

than the 2p (see p. 49) and so the overlap with the 2p orbitals which form the

carbonyl m system is poorer (see p. 67) for chlorine than it is for nitrogen.

Bonding in extended systems — conjugation

166

1@) \

C—Cl

H Fig. 10.27 Surface plots of the x MOs of methanoyl chloride; the molecule is viewed from the side with the C-Cl bond going to the right and the C—O bond going away from us and to the left. Note how there is little contribution from the chlorine 3p orbital to the 12 MO, indicating that the chlorine lone pairs are not participating in the 7 bonding.

We have shown the surface plots for the simplest acyl chloride, methanoyl chloride. However, it should be noted that this molecule is only stable at low

temperatures and is not usually encountered as a laboratory reagent.

The surface plots of the x MOs in methanoyl chloride (HCOCI), shown in

Fig. 10.27, support this explanation. The 12 MO results in bonding between the carbon and the oxygen, but this surface plot shows no contribution from

the chlorine. The 277 MO is mainly just the 3p AO on chlorine. Compare these

orbitals with those for methanamide (Fig. 10.18 on p. 161) which show the

nitrogen orbital participating in the 7 system. Overall, it is clear that the chlorine orbitals are not affecting the bonding

in the 7 system and so the conjugative effect is minimal. This, then, is the explanation for the high reactivity of the acyl chloride. In summary, there are two effects, illustrated in Fig. 10.28, of the substituent X on reactivity: e the inductive effect involves the electron-withdrawing nature of X increasing the positive charge on the carbonyl] carbon and hence increasing its reactivity;

e the conjugative effect involves the delocalization of the lone pair from X into the carbonyl system thereby raising the energy of the LUMO reducing the reactivity. O

il

R~ SX inductive effect

O

o

R~ x

Aw Sx

Ci

and so

|

conjugative effect

Fig. 10.28 An electronegative substituent X has two effects: firstly, it withdraws electrons from the carbonyl carbon, thus increasing its reactivity (inductive effect); secondly, its lone pair is delocalized into the carbonyl 7 system, thus decreasing its reactivity (conjugative effect).

Amides and esters

The reactivity of esters falls between that of amides and acyl chlorides: an ester is readily hydrolysed by refluxing with dilute alkali, whereas the hydrolysis of an amide requires much stronger conditions, i.e. higher temperatures and

longer times. Both reactions start with nucleophilic attack by hydroxide on the

carbonyl, as shown in Fig. 10.29.

10.3.

Chemical consequences — reactions of carbonyl compounds

O

HO NP Cw

HO

——>

R

OR'

R

e)

HO

HO

E\I-P Cc

R

\/ on

NH>

a“ae™N

a

R~

Cc

/

O°

>

O

>

OR'

R~

me

O° ~NHo

—_>

167

—_>

T

oO

T

Cc

a7

Ne

+

R'OH

+

NH3

Fig. 10.29 Both esters and amides are hydrolysed by aqueous alkali and both reactions are initiated by nucleophilic attack on the carbonyl by hydroxide. However, whereas the ester is readily hydrolysed under mild conditions, hydrolysis of the amide needs ‘stronger’ conditions, i.e. prolonged heating.

The lone pair on the oxygen in an ester can interact with the carbonyl 2 orbitals to form a delocalized system, just as in the case of an amide. The result is that, as was illustrated in Fig. 10.19 on p. 161, the LUMO is raised in energy thus reducing the reactivity of the carbonyl group.

Figure 10.30 compares the effect of conjugation with a nitrogen versus an oxygen lone pair; as we have noted before, the lone pair on the oxygen is lower in energy than that on the nitrogen, as is shown in (b). Clearly, the nitrogen lone pair has a better energy match with the carbonyl 2* MO than does the oxygen, so we expect the 32 MO to be raised in energy more in the case of the

amide than of the ester. Since it is this raising in energy of the LUMO which is responsible for the reduced reactivity of the amide, we conclude that the ester

should be more reactive than the amide. The inductive effect will also point to the ester being more reactive than

the amide as the oxygen is more electron-withdrawing than the nitrogen. Thus, both the conjugative and inductive effects work together to make the ester more

reactive than the amide, which is what we observe.

However, esters are still less reactive than acyl chlorides despite the inductive effect of the electronegative oxygen substituent. We therefore conclude

that there must be significant delocalization of the oxygen lone pair in the ester in order to account for this reduction in reactivity.

(@) CO n*

3g {

COn

:

co

‘

f

(b)

5 4

Hh

;

i

CO n*

-

2n

.

.

5 4

nH :

COn

N

amide

oe)

4U

3n

5 -

“——— i

2p

O

ester

Fig. 10.30 MO diagrams showing the interaction between the lone pair on nitrogen or oxygen with a system of the carbonyl group. Diagram (a) is identical to that of Fig. 10.19 and is appropriate for amide; note how the interaction with the lone pair raises the energy of the LUMO (37). Diagram shows how the situation is modified for an ester; the oxygen lone pair is lower in energy than that nitrogen, and so has a poorer energy match with the 7* MO,

the an (b) on

resulting in a smaller rise in the energy

of the LUMO (37). On this basis, we wouid predict that an ester will be more reactive than an amide.

168

Bonding in extended systems — conjugation

C-O bond lengths in carbonyl compounds When discussing the effect of conjugation of the nitrogen lone pair in amides we noted that good evidence for this was the shortening of the C—N bond length (Fig. 10.20 on p. 162). Now that we have discussed a range of other carbonyl compounds it is interesting to compare their C—O bond lengths and see how

they can be rationalized in terms of the bonding models we have developed.

The data are given in Fig. 10.31.

1.187%

“i

HsC~

O C

1.206.

Cl

“i

H3C~

O C

™

OCH3

1.213.

™T

H3C~

0 C

1.220. ~CH3

0 om

“I

~—-H3C

NH»

conjugative effect becoming dominant inductive effect becoming dominant Fig. 10.31 C—O bond lengths, in A, for a series of different carbonyl compounds.

The amide shows the longest C-O

bond and we have already described

(p. 162) how this can be attributed to the involvement of the nitrogen lone pair in the carbonyl z system. The ester has a shorter bond than the amide, and this is consistent with the view that the oxygen lone pair participates less in the z system than does the nitrogen lone pair, as was described on p. 167. The acyl chloride has the shortest bond, and we can rationalize this by recalling from p. 165 that there is very little participation by the chlorine lone pair in the z system, and hence none of the weakening of the C-O bond seen in amides. The z bond is therefore just a 2c-2e bond between the carbon and the oxygen. However, the story is a little more complicated than this, as we see that the C—O bond in the acy] chloride is actually shorter than the bond in the ketone. In this molecule there are no lone pairs to be involved in the z system, SO we can take the C—O bond length in the ketone to be unaffected by conjugation. What

is going on here is that the inductive effect is responsible for the shortening of the C—O bond; we will leave the explanation of why this is to the next chapter where the story is taken up again in Section 11.2 on p. 176. In summary, the trend of bond lengths shown in Fig. 10.31 is nicely explained as resulting from a balance between the conjugative effect, which leads to lengthening of the bond, and the inductive effect, which leads to shortening of the bond.

10.4

Stabilization of negative charge by conjugation

In water, a carboxylic acid dissociates to a significant extent, giving H30* and

the carboxylate anion; in contrast, simple alcohols dissociate to such a small

extent that they are not thought of as even weak acids (Fig. 10.32).

In both cases it is an O-H bond which is being broken, but the crucial difference is that in the carboxylate ion the negative charge is conjugated with

the carbonyl m system and is therefore delocalized on to both oxygens.

No

such delocalization is possible for the anion formed from the simple alcohol.

10.4

Stabilization of negative charge by conjugation 4

R— q

+

HsO

Pg o

=

OH

R-OH

169

+

H30

R-O

+

4H,0°

\y (-)

+

H0

===

®

_—R-C ‘

Fig. 10.32 Carboxylic acids dissociate quite readily in water to give the delocalized carboxylate ion {see Fig. 10.15 on p. 159). In contrast, simple alcohols hardly dissociate at all; we can attribute the

difference to the extra stability of the delocalized carboxylate anion.

It seems clear, therefore, that the delocalization possible in the carboxylate ion is responsible for stabilizing this ion. In this section we will explore why this is SO. The origin of this stabilization is that the lone pair of electrons on the oxygen (formally the negative charge) becomes involved in the carbonyl 7 system. If we concentrate on just the p orbitals of the carbon and the two oxygens we can draw up a simple MO

scheme, shown in Fig. 10.33, which explains how

this stabilization comes about.

(a)

bb)

CO n*

ag

CO n*

+

2p

co os

Cc=0

‘

2n oo CO n i

O-

7

C=O

2p

i

Oo

Fig. 10.33 Illustration of how the interaction of a negative charge, located in an oxygen 2p orbital, with an adjacent carbonyl! x system results in a lowering of the energy. Diagram (a) shows the situation with no interaction and (b) shows what happens when the orbitals interact; there is a decrease in the total energy of the occupied orbitals. The exact energy of the 27 MO is somewhat uncertain but it is expected to be close in energy to the oxygen 2p.

In Fig. 10.33 (a) we are supposing that there is no interaction between the

two 7 MOs and the out-of-plane 2p orbital. This orbital has two electrons in it, as both electrons from the O-H bond are left behind on the oxygen when the bond breaks to give Ht. In (b) the 2p orbital is now allowed to interact with

the x MOs and this gives rise to three MOs; in fact what we have here is three

2p orbitals in a row, so the three MOs are similar to those given in Fig. 10.16

on p. 159. Although the pair of electrons originally in the 2p orbital do not change energy very much as they move into the largely non-bonding 27 MO, the other pair of electrons are lowered in energy as they move into the I MO. Overall, therefore, the interaction leads to a lowering of the energy.

It is interesting to compare the carboxylate ion with two ions in which the

oxygens are replaced by CH? groups:

replacing one oxygen gives an enolate

anion and replacing two gives an allyl anion which we have already described on p. 157.

Bonding in extended systems — conjugation

170

The enolate anion is generated by treating an aldehyde or a ketone with a

strong base; this can remove one of the protons on a carbon adjacent to the

. carbonyl, leaving a negative charge as shown in Fig. 10.34 (a). As in the carboxylate ion, the charge is delocalized arid this is illustrated in the diagram by

the use of resonance structures.

Removing a proton from a carbon adjacent

to a C=C double bond also gives a delocalized anion (an allyl anion) which iS shown in Fig. 10.34 (b).

(a)

ty

fe)

R

EX

I

Nowsa

stron t

base

C)

oO

©

R7 ~e"

H

H

(b)

Ve R

ox

“~~

R

Cx!

H

aa aH

very ry stron strong

base

R~

H

H

enolate

5

CHp ’

yp

“6

CHe

Clo

~C~ H

H

R~

.

Sc

H

|

allyl anion

Fig. 10.34 An enolate anion is formed by removing one of the protons on a carbon adjacent to a carbonyl group, as shown in (a). Removing one of the protons from a carbon adjacent to a C=C double bond gives an allyl anion, as shown in (b). Both anions are delocalized, but the enolate has a resonance form in which the negative charge appears on an electronegative element, oxygen. This confers extra stability and so explains why the enolate anion is much easier to form than the allyl anion.

Comparing the two anions, we can expect that the enolate will be lower

in energy as the negative charge can be delocalized onto the electronegative

oxygen atom. Although the allyl anion is also delocalized, there are no electronegative atoms onto which the charge can be delocalized. This explains why we need a much stronger base to form the allyl anion than is needed to form the enolate. We have a nice progression here involving these three anions. The carboxylate, in which the negative charge can be delocalized onto two oxygens, is

the most stable of the three. Next comes the enolate, in which delocalization

onto one oxygen is possible, and finally the allyl anion in which there are no electronegative atoms.

Stabilization by larger 7 systems

If the negative charge is conjugated with a more extensive 7 system then the charge can be delocalized onto more atoms and this is found to confer extra stability. In general, the more delocalized the charge becomes, the greater the stabilization. A good example of this is the anion formed by the ionization of the O-H in

phenol; as shown in Fig. 10.35, the resulting negative charge can be delocalized

round the benzene ring. The extra stability which this delocalization gives the

anion accounts for the observation that simple alcohols (such as ethanol) are

not acidic to a significant extent whereas phenol is a weak acid (indeed, it

10.4

171

Stabilization of negative charge by conjugation

used to be known as carbolic acid). The anion formed when a simple alcohol dissociates is not delocalized, whereas that from phenol is.

OH

0°

O

O (Ss)

O (S)

ic)

Fig. 10.35 The phenolate anion, formed by the dissociation of phenol, shows extensive delocalization

of the negative charge into the benzene ring. This confers extra stabilization and so accounts for phenol being a weak acid, in contrast to simple alcohols which are not significantly acidic.

Figure 10.36 shows the HOMO of this phenolate anion. Comparing this to the resonance structures shown in Fig. 10.35 we see that the carbons on which the negative charge appears are precisely the ones whose 2p orbitals contribute

to the HOMO.

Fig. 10.36 Surface plot of the HOMO of the phenolate anion, whose resonance structures are shown in Fig. 10.35; the oxygen is on the left, coming towards us. Note how the atoms whose AQOs contribute significantly to this MO are the same as those onto which the negative charge can be delocalized.

Substitution and elimination

11

reactions ny

At the end of Chapter 9 we described that when a nucleophile replaces the bromine atom in t-butyl bromide, (CH3)3CBr, the rate is found by experiment to be first order and independent of the concentration of the nucleophile

rather than second order (i.e. proportional to both the concentrations of the bromoalkane and the nucleophile) as is observed with bromomethane: first order: (CH3)3CBr + Nu~

—>

(CH3)3CNu+

Br

—>

CH3Nu + Br-

rate = k[(CH3)3CBr]

second order:

CH3Br + Nu~

rate = k'[(CH3Br][Nu_].

We are now going to look more closely at these and other reactions using some

of the ideas from Chapter 10 to understand why the rate laws are different.

11.1.

Nucleophilic substitution revisited - Sy1 and Sy2

We have seen in Sections 7.5 on p. 107 and 9.1 on p. 131 how bromomethane and hydroxide react together in a single step to form the products.

For the

moment let us simply assert that the reaction between a nucleophile and t-butyl

bromide proceeds via a completely different two-step mechanism.

In the first

step, the carbon—bromine bond breaks to form a bromide ion and a reactive species, called a carbocation or carbenium ion, in which a carbon atom bears a positive charge. The curly arrow mechanism for this step is shown in Fig. 11.1. It is essentially the reverse of two ions reacting to form a neutral molecule as illustrated on p. 97 by the reaction of Ht and H7 ions.

(CHg)3C Lt Br

(CHg)sC ® Br

Fig. 11.1 The formation of a carbenium ion from t-butyl bromide.

The carbenium ion is very reactive and in the second step it quickly reacts

with the nucleophile to give the product. The curly arrow mechanism for this

step is shown in Fig. 11.2.

(CH3)3C

©

Nu

———»

(CH3)3C

—Nu

Fig. 11.2 The reaction between the carbenium ion and the nucleophile.

11.1

Nucleophilic substitution revisited — Sy 1 and Sx2

173

transition state 2

>

energy

transition state 1

intermediate carbenium ion

i"

Hgcyon

H3C

Nu®

Br

products

reactants

i Bre

HaCyN H3C —_ reaction coordinate

Fig. 11.3 An energy profile for the reaction between reaction occurs in two steps:

f-butyl bromide and a nucleophile,

the first is the formation of the carbenium

ion intermediate;

Nu~.

The

the second

step is the reaction between the carbenium ion and the nucleophile to give the product. The second transition state is lower in energy than the first.

Figure 11.3 shows an energy profile for the overall reaction. As the reaction between the positively charged carbenium ion and the nucleophile has such a small activation energy (F,2), the initial formation of the carbenium ion from the t-butyl bromide is the rate-determining step (see Section 9.6 on p. 141). The rate of step (1), the rate at which the intermediate carbenium ion forms,

depends only on the concentration of the t-butyl bromide — the more t-buty]

bromide there is, the faster the carbenium ion will be formed. We can write the rate of formation of the carbenium ion as: rate of step (1) = k;[(CH3)3CBr]. As soon as it has been formed, the carbenium ion reacts with the nucle-

ophile to give the products. Since the first step is rate-determining, it follows that the rate of formation of the product is the same as the rate of step (1): rate of formation of the product = k[(CH3)3CBr].

This mechanism therefore explains the observed first-order kinetics of the reaction of t-butyl bromide.

We have two possible mechanisms for these nucleophilic substitution reac-

tions. The reaction between bromomethane and the nucleophile depends on the concentrations of both reagents and proceeds by both reagents coming together

in a single step. This mechanism is known as an Sn2 mechanism: this stands for Substitution, Nucleophilic with the ‘2’ indicating that the rate-determining step involves both reagents and so the rate law is second order.

Substitution and elimination reactions

174 (a)

(b)

Nu

Nu—

ae

Fig. 11.4 Diagram (a) shows that the three hydrogen atoms in bromomethane do not hinder the approach of a nucleophile in the correct direction to attack the C—Br o*. In contrast, (b) shows that the methyl groups in t-butyl bromide prevent the nucleophile approaching. The dots in each picture are used to outline the approximate atomic radii of each of the atoms.

The reaction between t-butyl bromide and the nucleophile proceeds in two steps — the initial formation of a carbenium ion from the t-butyl] bromide followed by the fast reaction of this ion with the nucleophile. This mechanism is known as an SnI mechanism, the ‘1’ indicating that the rate-determining step

only involves one species i.e. this step is unimolecular or first order. The question we now need to address is why is there this change in mechanism? Why does bromomethane not follow the Sj 1 mechanism and form the cation CH}? Why does f-butyl bromide not react directly with the nucleophile following the Sy2 mechanism? The latter question is relatively easy to answer. We saw in Section 7.5 on p.

109

that in a reaction

following

the Sn2

mechanism,

the attacking

nucleophile must approach from directly behind the bromine leaving group.

Whilst this is possible for a nucleophile attacking bromomethane (as shown in

Fig. 11.4 (a)), for t-butyl bromide, this approach is severely hindered by the three methyl groups as shown in (b). The question as to why bromomethane does not undergo an Sn 1 reaction

has a more complex answer. Put simply, the answer is that the carbenium ion that would be formed from bromomethane, H3C*, is so high in energy that it cannot readily form. This contrasts with the (CH3)3C* ion which is much more

stable. It turns out that the methyl groups help to stabilize the positive charge

in the (CH3)3Ct ion whereas no stabilization is provided by the hydrogens in H3C?. Exactly how positive charges in ions may be stabilized in this and other ways is the subject of the' next section.

11.2

The stabilization of positive charge

We have seen in Section 10.4 on p. 168 how negative charge can be stabilized by delocalization, i.e. where the electrons are not confined to one atom but are

spread over many in a delocalized MO. Positive charges can be stabilized in

a similar manner but there is one important difference: positive charges them-

selves do not move. To understand this distinction we need to think carefully about what negative and positive ions are. A negative ion is simply a molecule (or atom) in which the number of electrons exceeds the total nuclear charge. For example, in BH, the total nuclear

charge is nine (five for boron, plus a total of four from the hydrogens) but there are ten electrons, giving an overall negative charge of one. Similarly, a posi-

11.2

The stabilization of positive charge

175

tively charged ion is one in which there are insufficient electrons to compensate

for the nuclear charge. For example, in NH7 the total nuclear charge is 11, but there are just 10 electrons. In a negative ion we can imagine the electrons mov-

ing from one atom to another as a result of delocalization — for example, in the

enolate anion shown in Fig. 10.34 (a) on p. 170 the negative charge can be on the carbon or the oxygen. In a positive ion the charge may also appear on different atoms. However,

this is not due to the positive nuclei moving but is due to the movement of the

negative electrons. The positive charge only appears to move as a result of the actual movement of electrons.

As with negative charges, the formation of a positively charged species is not generally favourable unless there are special factors to stabilize it, such as delocalization; it is this stabilization which we will discuss in this section.

The structure of CHT On p. 86 we described the bonding in the planar trigonal molecule BH3 using

sp” hybridization of the boron. There are three 2c-2e bonds formed by these hybrids, leaving an empty 2p orbital pointing out of the plane. The species CH} is isoelectronic with BH3, meaning that it has the same number of electrons; however, as the nuclear charge is one greater, the molecule has an overall positive charge. We can therefore use the same description for the bonding in CHj as we used for BH3; so the LUMO of CHy is a vacant 2p orbital, shown schematically in Fig. 11.5. We must not be tempted to say that the ‘positive charge is in the empty 2p orbital’; electrons occupy orbitals, not positive charges.

We saw in Section 7.2 starting on p. 98 that the presence of the empty 2p orbital in BH3 (the LUMO) makes it susceptible to attack by a nucleophile

which donates electrons from its HOMO into the BH3 LUMO. The same is true for CHT, but even more so, as the positive charge further increases the interaction with the nucleophile, especially if it is also charged. As a result,

CH}

is a highly reactive species which, if it could form in solution, would

only have a fleeting existence. Stabilization by adjacent lone pairs The interaction of CHF

with the HOMO

of the nucleophile gives us a clue as

to how the positive charge on carbon can be stabilized. Suppose that we make a pair of electrons available not from the HOMO of a nucleophile but from an atom attached to the carbon; to be specific, let us replace one of the hydrogen atoms with O~. Such a replacement gives us the rather odd looking species +CH2-O7 depicted in Fig. 11.6 (a). We can imagine that the negative charge on oxygen is located in a 2p orbital, which is of course adjacent to the empty 2p orbital on carbon. These two orbitals will interact to give a 7 MO — shown

in (b) — which is occupied by the two electrons. In other words, a 7 bond is formed. The two representations (a) and (b) are simply resonance structures of the same molecule, methanal, CH2=O as shown in (c).

The MO picture of this interaction is shown in Fig. 11.7; as we have noted

before, the lone pair on oxygen is lower in energy than the carbon orbital.

Interaction with the carbon orbital results in a 2 bonding MO which is lower in

His ho H

Fig. 11.5 The LUMO of CHj is the

out-of-plane 2p orbital.

Substitution and elimination reactions

176 (a)

filled O 2p orbital

(b)

(c) ‘

empty C 2p orbital Fig. 11.6 shown in electrons methanal,

Replacing one of the hydrogen atoms in CH with an O- gives the odd-looking species (a). The two 2p orbitals interact to form the x MO shown in (b); this is occupied by the two to give a x bond. The two forms are actually resonance structures of the same molecule, H2C=O, as shown in (c).

energy than the original orbital on oxygen. The lone pair of electrons move into

this orbital, thus leading to an overall lowering of the energy. We see, therefore, how having an adjacent lone pair leads to stabilization of the positively charged

carbon. Using a lone pair from a negatively charged oxygen is an odd way to stabi!

;

ot of

i 5

lize a positive charge on carbon — as we have seen, the net result is the formation of a neutral molecule with no positive charge at all. However, this example highlights that the stabilization results in the positive charge being no longer localized on the carbon, an idea which we will continue to explore.

.C-O x*

Le

i

tho

The stabilizing lone pair does not need to come from a negatively charged

atom; exactly the same effect is observed if an -OH group is used in place of the O~. At first glance, it might be tempting to say that the electronegative oxygen

rt

would destabilize an adjacent positive charge; this is not the case. Rather it is because the oxygen has relatively high-energy lone pairs which can interact

Fig. 11.7 MO picture showing how the energy of the system is lowered by the interaction of a lone pair on oxygen (shown on the left) with an empty orbital

on carbon (shown on the right).

R

vow

R

R

with an empty orbital in such a way that the charge is stabilized.

As Fig. 11.8 shows, a better way of drawing this species is as a protonated

carbonyl.

a“

R

Fig. 11.8 An OH group stabilizes an adjacent carbenium ion. A better representation of this ionis as a protonated carbonyl.

Whilst the unstabilized carbenium ion CH}

is far too reactive to

exist in aqueous solution, protonated carbonyl cations are formed when acid is added to a solution of the carbonyl compound. Experimental evidence confirms that the better representation of the cation is as the protonated carbonyl compound with the positive charge on the oxygen rather than on carbon. In forming the new C—O z bond, the donation of the

oxygen electrons lowers the energy of the system just as we saw in Fig. 11.7. The acylium ion We are now in a position to understand why the C=O

bond in an acyl chlo-

ride, such as ethanoyl chloride, is so short, as mentioned on page 168. If ethanoyl chloride is mixed with silver tetrafluoroborate in an inert solvent such as nitromethane (CH3NOz) at low temperatures, silver chloride precipitates out

leaving a solution of the salt [CH3CO]* BF, : CH3COC] + AgBF4y —>

Fig. 11.9 A possible mechanism for the formation of the acylium cation.

[CH3CO]* BF, + AgCl(s).

The reaction is driven by the precipitation of the insoluble silver chloride. It might be tempting to think that the structure of the cation is just like ethanoyl chloride minus the chloride ion as shown in Fig. 11.9. However, the crystal structure of the salt has been determined and the cation turns out to be linear

11.2.

The stabilization of positive charge

177

with a C—O bond length of 1.108 A, notably shorter than the C-O bond length

in ethanoy! chloride at 1.187 A. Once the chloride ion has departed, there are only two atoms or groups around the carbonyl carbon in [CH3CO]*, the methyl group and the oxygen; it should therefore be no surprise that these are at 180° to each other. We now

have just the situation described above with a positive charge, nominally on the

carbon atom, and an adjacent oxygen atom. The oxygen atom can stabilize the positive charge by donating a pair of electrons. This is shown in Fig. 11.10. ‘. @ O=C—CHs3

=~,

@ :0=C—CH3

Fig. 11.10 The positive charge on the carbon is stabilized by the donation of a pair of electrons from the adjacent oxygen atom.

The donation of the lone pair from the oxygen formally creates a triple bond between the oxygen and carbon which explains the shortening of the bond length. The acylium ion plays an important role in a number of reactions

such as the acylation of aromatic rings.

The way in which the bond length is shortened in the acylium ion allows us to understand why the CO bond in ethanoy] chloride is shorter than in other carbonyl compounds. Whilst ethanoy] chloride does not exist as the separate acylium and chloride ions, the chlorine is electronegative and withdraws some electron density towards itself, increasing the partial positive charge on the carbony] carbon as mentioned on p. 168. This in turn brings down some electron

density from the oxygen lone pairs, strengthening the CO z bond as shown in Fig. 11.11. Comparisons of the CO bond lengths in propanone, ethanoy! chloride and fluoride and the acylium cation are shown in Fig. 11.12. We have already described how the electron-withdrawing chlorine leads to a shortening of the CO

bond.

Changing chlorine to the even more electronegative fluorine results in

Fig. 11.11 The electronegative chlorine withdraws electrons from the carbon, thereby making it slightly more positively charged and this, in turn, brings down more electron density from the oxygen, thereby strengthening the C=O m bond.

further shortening of the bond. Finally, in the acylium cation, there is essentially a triple bond between the carbon and oxygen, giving a further reduction

in bond length.

12138. HsC~

Oo C

1187. ~CHs

HsC~

oO

1160. Cl

0 HsC~

1.108 F

0° LL 3

Fig. 11.12 Along the series propanone > ethanoyl chloride — ethanoyl fluoride the partial positive charge on the carbonyl carbon increases leading to a decrease in the CO bond length (shown in A). The acylium cation with its full positive charge has one of the shortest CO bond lengths known.

Stabilization by adjacent 7 systems Other atoms with lone pairs, such as nitrogen, can stabilize positive charges in the same way that oxygen does but if no lone pair is available, then other filled orbitals may help to stabilize the positive charge. We saw on p. 96 that generally after a lone pair, the next highest energy orbital, and hence the next best for stabilizing a positive charge, is a x MO. An example of stabilization by such an MO is the allyl cation shown in Fig. 11.13 where the positive charge is stabilized by a neighbouring C=C.

|

ANE"

|

H

H

Fig. 11.13 The allyl cation. The positive charge is stabilized by the adjacent 7 bond.

Substitution and elimination reactions

178

3n

oe

C-Cnt

OO

C-Cr

sO

me

Fig. 11.14 MO diagram showing how the positive charge interaction with the adjacent x system. The C=C and on the adjacent carbon to give three MOs. The lowest, orbitals. Since this is the only orbital occupied, the energy non-bonding and 37 is anti-bonding.

on carbon in the allyl cation is stabilized by x* MOs interact with the vacant p orbital 17, is lower in energy than the combining of the system has been lowered. MO 27 is

In the allyl cation we have a 2 system formed from three p orbitals: two can be thought of as originating from the C=C z bond and one is the vacant orbital

on the adjacent carbon. We have already described in Fig. 10.11 on p. 158 the three MOs which arise from the interaction of these three 2p orbitals; the MOs

are depicted once more in Fig. 11.14. In this figure we imagine that the three MOs arise from the interaction of the C=C 2 and 2* MOs with the 2p AO on

the adjacent carbon. For example, the 12 MO can be thought of as arising from an in-phase interaction between the 2p and the C=C m MO. Overall though, the final result is just the same as for three p orbitals overlapping in a line. Of these MOs, only the Iz is occupied and this clearly results in a lowering

of energy as the electrons move from the C=C m2 MO. The interaction with the adjacent w system therefore results in a lowering of the energy — we say that the positive charge is stabilized. It is interesting to note that it is the electrons in the 7 system which are lowered in energy by the interaction with an empty orbital, thus stabilizing the molecule.

In Fig. 10.14 on p. 159 we saw how the allyl anion could be represented by two different resonance structures or a delocalized structure. The allyl cation may be represented in an analogous manner as shown in Fig. 11.15. H

Ce =2a™~

Hc“

f CH

=o

@/C

Hoo™

H

(+) CH,

H

a

HoC*~

LC.C

(+) CH

Fig. 11.15 On the left, connected by a double-headed arrow, are two resonance structures for the allyl cation. On the right is an alternative representation in which the dashed line shows the partial x bond across all three atoms; the atoms onto which the positive charge can be delocalized are indicated by (+).

11.2

The stabilization of positive charge

179

Stabilization by adjacent o bonds - o conjugation

If there are no lone pairs or 2 bonds adjacent to the positive charge, the cation

can still be stabilized by the electrons in neighbouring a bonds. This type of stabilization is called o conjugation. In order for the o bond to help stabilize the cation, it must be in the correct

orientation. We saw how lone pairs and when their occupied MOs

bonds stabilize the positive charge

overlap with the vacant p orbital on the carbon;

effective overlap can only occur if the orbitals involved are in the same plane. The same is true for 0 conjugation — the o MO must be in the same plane as the vacantp orbital as shown in Fig. 11.16 (a).

(@)

filled C-H o orbital ®\

C)

(b) constructive CQ

Goce,

y's:

destructivea)

empty C 2p orbital

!

Fig. 11.16 In order for an adjacent o bond to help stabilize a cation, the « MO must be able to get into the same plane as the vacant p orbital. This has been achieved in (a) where the C-H o MO involves the carbon atom next to the one with the positive charge. In the case of CHS, shown in (b), the only « MOs are at right angles to the vacant p orbital and so no net overlap is possible.

If the orbitals can overlap, they interact as shown in Fig. 11.17. The electrons in the 0 MO are now more delocalized and hence lowered in energy. It is this lowering in energy of the electrons in the o MO that stabilizes the cation.

Figure 11.18 shows the delocalized MO formed essentially from the interac-

tion between the C-H o MOs and the vacant p orbital. It clearly shows that some electron density is shared between the two carbon atoms.

Fig. 11.18 A delocalized

MO

formed

from the interaction between

the C-H

o MOs

orbital; the electrons can be found in the region between the two carbon atoms. lowers the energy of the cation.

If the

a MOs

and the vacant p

This delocalization

cannot get into the same plane as the vacant p orbital then

no stabilization is possible. This is the case in the CH} cation; the C-H bonds are at right angles to the vacant p orbital and consequently no net overlap is possible as illustrated in Fig. 11.16 (b). The o MO need not be from a C-H bond; a C-C bond, for example, can also stabilize the cation. The degree of stabilization by o conjugation is not

as significant as conjugation involving a lone pair or 2 bond. The reason for this is that o MOs are lower in energy than both lone pairs and 7 MOs and so the degree of overlap between a 0 MO and a vacant p orbital will be less than

.

2p c®

Fig. 11.17 The interaction between the o bonding MO and the vacant p orbital lowers the energy of the electrons in the

o MO, thereby stabilizing the cation.

180

Substitution and elimination reactions between the lone pair or 7 MO and the vacant p orbital. However, the more a conjugation that is possible, the more stabilized the cation will be. This finally explains the mystery we started this chapter with: why f-buty]

bromide undergoes a substitution reaction by first forming the carbenium ion

whereas bromomethane follows the Sy2 mechanism instead. In the (CH3)3Ct ion, C-H o MOs from each of the three methyl groups are able to conjugate with the vacant p orbital. Figure 1'1.19"shows a delocalized MO where the Pp orbital on the central carbon is o conjugated to all of the C-H MOs, spreading electron density over the whole molecule. The large amount of o conjugation possible in this ion is sufficient for it

to be relatively stable and so be formed readily.

Fig. 11.19 A MO in the carbenium ion,

(CH3)3C*, showing the extensive

delocalization due to the « conjugation.

In contrast, for CH}

no a

conjugation is possible and hence this cation does not form. So on the grounds

of the stability of the carbenium ions, the Syl mechanism is disfavoured for CH3Br and favoured for (CH3)3CBr.

The degree to which o conjugation is possible explains the observation

that the more alkyl groups around the central cation, the more stable the ion, as

shown in Fig. 11.20. ©

@

H—cwh H

Hac — Cw" H

®

(o)

Hyco — Cw" CH H

Hac — cus CHs

Increasing degree of o conjugation possible Increasing stability of cation Fig. 11.20 The more alkyl groups attached to the positive carbon, the more « conjugation is possible and hence the more stable the carbenium ion.

11.3

Elimination reactions

Mixing a nucleophile, such as cyanide, CN~, with t-butyl bromide gives the ex-

pected substitution product (CH3)3C-CN. However, adding hydroxide (which we might think of as being a typical nucleophile) to t-butyl bromide does not yield (CH3)3C—OH but instead an alkene, isobutene (2-methylpropene), as

shown in Fig. 11.21. Rather than the expected substitution reaction occurring, what we see is an elimination reaction in which the net result is that HBr has

effectively been lost (eliminated) from the t-butyl bromide (no HBr appears in

the products since under basic conditions water and bromide ion are formed). CHg

|

HC ON

CHa wi :

H3C'¢

Br

+ OH

H3C

aK 3

H3C

OH

~_N C=CHe

+

+

iC}

io}

Br

Br

+ HO

Fig. 11.21 The reaction between f-butyl bromide and hydroxide does not yield the expected alcohol but instead an alkene, isobutene.

11.3

181

Elimination reactions

Let us suppose for the moment that in the elimination reaction the initial step is as we outlined above, namely the formation of the relatively stable trimethylcarbenium ion, (CH3)3CT. Why does hydroxide not react with this to form the substitution product (CH3)3C—OH? We can gain a clue to understanding this by looking again at the delocalized MO of the trimethylcarbenium ion

shown in Fig. 11.19. The orbital shows that there is electron density spread out over the whole of the ion; this delocalization has a number of important consequences. The delocalization removes some electron density from the C-H

and shares it between the two carbons. C—H o MOs

0 MOs

Removing electron density from the

means that these o bonds are weakened.

However, the C-C bond

is being strengthened since it gains some partial 7 character. This accounts for

the fact that the C—-C bond is shorter in the cation than in the neutral hydrocarbon as illustrated in Fig. 11.22. If we continued this withdrawal of electrons from one of the C-H o bonds

to the extreme, eventually all of the electron density from the o bond would end up being shared between the two carbon atoms. In other words, eventually

there would be a full C-C m bond and a free proton, Ht. This process is illustrated in Fig. 11.23 where the stabilizing interaction between the C-H o bond and the vacant p orbital is shown in (a) and the result of taking this to the

extreme is shown in (b). The corresponding curly arrow mechanism is shown in the lower part of the diagram.

The mechanism forming the alkene in Fig. 11.23 is not realistic — the car-

benium ion does not spontaneously form the alkene and a proton in solution. Indeed, as we shall see later, the reverse is true — a proton will attack the alkene to form the cation. Nonetheless, the 0 conjugation does weaken the C—-H bond and this means that the hydrogen becomes more acidic. This gives us the clue as to what happens when a base (such as hydroxide) is added. In order to form the substitution product, the incoming hydroxide has to reach the central carbon. Although this is possible, the approach is crowded

by the hydrogens — see Fig. 11.24 (a) — and in fact the hydroxide reacts preferentially with these.

NC—Ca"

17®@ @ empty

Py

K

Remember that these hydrogens are, as a result of the

CH

3

C 2p orbital

CV ech

Hwyo—C CH

Hii)

i

Ao

i CH

“

filled C—C nr orbital

H®

Hinge yc

gun

“CH

H Fig. 11.23 The interaction between the C-H « MO and the vacant p orbital is shown in (a). If carried to the extreme, this would eventually lead to the complete formation of a C-C m bond and a free proton shown in (b). The lower part of the diagram shows the curly arrow representation of the same process.

|

H3C7h

8

Cu 'CH ~~

W'S

1.54A

CH;

Fig. 11.22 The delocalization in the trimethylcarbenium ion shortens the C—C bond length relative to that in the hydrocarbon.

Substitution and elimination reactions

182 (a)

(b)

HO

HO

-)

Fig. 11.24 Rather than squeeze past the hydrogens to attack the vacant p orbital on the carbon as shown in (a), the hydroxide just helps to take off the already acidic hydrogen as shown in (b).

@ conjugation, somewhat acidic and so all that happens is that the OH™

ab-

stracts one of these hydrogens (as H*) to give water and the alkene as shown in Fig. 11.24 (b). The corresponding curly arrow mechanism for this reaction is shown in Fig. 11.25.

H—o” ) f

H—O, (3)

wiC—CX ~ uCH 30 CH,

H HungmcounCHs

HH

H

a)

"CHs

Fig. 11.25 The reaction between the trimethylcarbenium ion and the strong base hydroxide to form the elimination product, isobutene.

We have seen that, instead of forming t-butyl alcohol, hydroxide ion reacts with t-butyl bromide to give isobutene. It is possible to form t-butyl alcohol from the bromide but we cannot use hydroxide since it is too strong a base.

Using water instead of hydroxide will form more of the desired substitution product, although some of the alkene will still form. Water is less basic than hydroxide and therefore not so good at removing the acidic hydrogens from the cation. However, it is still perfectly able to react with the reactive trimethylcarbenium ion. The curly arrow mechanism for the reaction of the trimethylcarbenium ion with water is shown in Fig. 11.26. H

H

-O

‘

| Ge

H

~)

Hac 3

—SunCHg NCH,

oT,

H

H

iV

HaC~

b

Stn,

Von’

a

el

()]

H3C~

rox

|

H

an

NV Gis

:

3

Fig. 11.26 The reaction between the trimethylcarbenium substitution product, t-butyl alcohol.

ion and the weak base water to form the

Bases and nucleophiles

As we have seen, in its reaction with a halogenoalkane,

hydroxide can act

either as a nucleophile and substitute for the halogen, or it can act as a base by removing a hydrogen ion. In a way, it is unfortunate that we have two separate words for this behaviour since it encourages us to think that there is

11.4

183

Addition reactions — elimination in reverse

a fundamental difference in the way the hydroxide reacts; there is not. When acting as a base, hydroxide (or any other base) is carrying out a nucleophilic

attack but specifically on an H—-X bond rather than on a C—X bond. All that is needed is for the base/nucleophile to possess a high-energy pair of electrons, usually a lone pair. The base/nucleophile could be charged, like OH~ or NH; or neutral, like NH3. The idea that a base is a hydrogen ion acceptor and that an acid is a hydrogen ion donor, is known as the Brgnsted-Lowry theory, named after Johannes Brgnsted and Thomas Lowry who independently proposed these ideas in the

1920s. A more refined definition of acids and bases was proposed by Gilbert

N. Lewis: a Lewis base is a species which is a good donor of electrons whilst a

Lewis acid is a species which can act as an electron acceptor. The Lewis definition of a base removes any distinction between something acting as a base or as a nucleophile! It is true that some substances are better at removing hydrogen ions than attacking at other centres; an example being inorganic amides such as sodium

amide,

Nat NH;

or lithium diisopropylamide, Lit N[CH(CH3)2]3 . Other sub-

stances, such as iodide, I~, are good nucleophiles but poor bases.

Most sub-

stances can (and do) act as both nucleophiles and bases.

Exactly why something prefers to attack an H—X bond and remove a hydro-

gen ion, rather than attack any other centre, depends on a number of factors;

these may include the energy of its lone-pair electrons, which other groups or counter-ions are present, what solvent is used and, of course, exactly what it is

reacting with. These ideas wil] be explored in the future chapters. 11.4

Addition reactions — elimination in reverse

We mentioned above that whilst it is fairly easy for a base such as hydroxide to remove a hydrogen from the trimethylcarbenium cation, the Ht will not

spontaneously fall off to give an alkene.

We are now going to look at the

reverse reaction, adding H* to an alkene to form a carbenium ion, specifically

we shall look at the protonation of isobutene to form the trimethylcarbenium ion.

On p. 101 we saw that in trying to understand how two reagents might react,

we should first identify the highest energy occupied MO of the whole system and then the very lowest energy unoccupied MO. Treating our acid as a source

of H+ means that the LUMO must be from this species as it has no electrons; we will assume that this orbital is a 1s AO. The highest energy electrons must therefore come from the alkene. There are no lone pairs in the alkene — the HOMO is the C-C xz bonding MO.

The problem is, for an unsymmetrical alkene like isobutene, there are two positions in which the incoming Ht could end up being bound, as shown in Fig. 11.27. In route (a), the proton adds to the /east substituted carbon atom, meaning

that the positive charge ends up on the carbon atom with the most substituents.

Protonation on the other carbon, as shown in route (b), means that the positive charge ends up on the least substituted carbon. We have seen on p. 180 that the

Substitution and elimination reactions

184 (a)

®

ral

Hey

1C=C}h

H™

(b)

wiCH

NCH

3

®H

‘

H

‘\

—_—

®@

wic—C

ou ’

Hi JC=Ch wtCH 3

‘CH

H”

ee

wiiCHs

‘CH; H

Hey 1C—Cu,

———_>

Yorn’

HY

Fig. 11.27 An unsymmetrical alkene, such as isobutene, may protonate in either of two positions. {n (a) the proton adds to the carbon atom with the most hydrogens and results in the positive charge forming on a carbon which has three methyl groups attached. In (b) the proton adds to the carbon with two methyl groups and results in the positive charge forming on a carbon with just one alkyl group attached. Route (a) is the preferred choice since this forms the most stable carbenium ion.

most stable cation will be the one where the most o conjugation is possible.

Since hydrogens attached to a positively charged carbon atom cannot stabilize the cation but adjacent C-H or C-C o bonds can, the most stable cation will be the one with least hydrogens attached to the positive carbon. Looking at it the

other way round, the most stable carbenium ion is the one in which the positive

carbon has the greatest number of stabilizing alkyl groups attached to it.

Once the carbenium ion has been formed, it will react with any nucleophile present, as shown in Fig. 11.28. This is exactly the same mechanism we saw in our discussion of the Sn 1 mechanism.

H

3

Cc—cuncHs C

—_—_

H

3

oo,

Cc ‘ny CH

CH3 Fig. 11.28 The trimethylcarbenium ion will quickly react with any nucleophile present.

Overall in this reaction H™ is first added to the alkene followed by attack by

H3C H3C

a nucleophile. For example when isobutene is mixed with hydrobromic acid,

H ‘c=c /

HBr, the first step is for the alkene to be protonated to give the trimethylcarbenium ion and then this is attacked by bromide ion giving t-butyl bromide. Such reactions are examples of addition reactions. As Fig. 11.29 shows, addition

H

reactions are simply the reverse of elimination reactions.

‘

— HBr

+ HBr

elimination

addition

Markovnikov’s Rule

The observation that the proton adds to the carbon with the greater number of

hydrogens attached, is sometimes known as Markovnikov’s rule after the Rus-

Br

Hsc'4 HC

sian chemist, Vladimir Markovnikov, who first formulated the rule. However,

H —

~

CN

H

Fig. 11.29 Addition of HBr to isobutene is the reverse of the elimination of HBr from

t-butyl bromide.

sometimes the rule breaks down. A better version of the rule would be to say that the proton adds to the carbon atom of the alkene that gives rise to the most stable cation.

The reason for this slight modification is that, as we have seen

above, other groups are better at stabilizing positively charged carbon atoms than simple alkyl groups. An example of the application of this modified rule is shown in Fig. 11.30.

11.5

E2 elimination

HC6s+.

6 8 LON Cc

Hl ~O7

185

(ie

protonate

CHp

on carbon 1

HC.sb~

27

26

i

“GHe

C

CH>

H~ 1 >0O7

protonate

HaC\Ne LC “ow

on carbon 2

Cc

~CHe

H~o~Q7

CH

Fig. 11.30 The structure in the centre can be protonated on either C; or Co. Protonating Cj gives a carbenium ion which is stabilized by a conjugation alone; protonating Co gives a carbenium ion which is stabilized by the neighbouring oxygen atom. The oxygen is much better at stabilizing the charge and so the molecule is protonated preferentially on Co.

The structure in the centre can protonate on either C; or C2. C; has more

hydrogens attached than C2 which has none and so Markovnikov’s rule would

suggest that protonation occurs on C;. Protonating C; does give a carbenium ion which can be stabilized by o conjugation, but protonating C2 gives a carbenium ion with a neighbouring oxygen atom. Remember (see p. 176) that an adjacent oxygen atom stabilizes a positive charge very effectively — much more so than just o conjugation alone — so this molecule does protonate preferentially on C2. A better way of representing the protonated product is shown

in Fig. 11.31 where the oxygen has donated one of its lone pairs and formed a mz bond between the C and O. So in this example the molecule does not pro-

tonate on the carbon with the most hydrogens attached but so as to give the most stable cation. Understanding the rule is always better than just applying

it blindly! 11.5

E2 elimination

We have seen how t-butyl bromide can eliminate HBr by first losing a bromide ion to form the stable carbenium ion and then having a proton removed to form the alkene. HBr can be eliminated from the other bromoalkanes to give alkenes; for example, 1-bromopropane forms propene when mixed with hydroxide as shown in Fig. 11.32.

H3c~

~C~

——*

HC

H Cc ~

Sct 1,

+ Br

S)

+ H20

Fig. 11.32 Hydroxide reacts with 1-bromopropane to give propene.

However, a carbenium ion could not form from 1-bromopropane since there

would be insufficient o-conjugation in the CH3CH2CH; ion for it to be stable (see Fig. 11.20 on p. 180). We therefore need to find an alternative mechanism for the elimination which does not involve the formation of this ion. We saw on p. 181 that the reason why a base can remove one of the protons

from the trimethylcarbenium ion was that the interaction of the C-H

0 MOs

with the vacant p orbital weakens the C-H bonds making the hydrogens more

acidic. In 1-bromopropane, there is no vacant p orbital for the C-H o MQOs to interact with.

However, the vacant C-Br o*: MO

can interact to some degree

with the C-H 0 MOs. The C-Br o* is not as low in energy as a vacant p orbital so the energy match between this and the filled C-H o MO is not so good. Nonetheless, if

Fig. 11.31 After protonating on C» the carbenium ion is stabilized by the oxygen as shown

in this structure.

Substitution and elimination reactions

186

(b)

(a)

e Be

@.

lone pair of base O

es Yo,

Hs Cv

C-H

o

_- new o bond between base and proton NY

orbital

SH

ny

,

@..

/%

filled C-C x orbital

empty C—Br o* orbital

lone pair of bromide

al

aH

cys SQjn H

too

>

SH

Br

Fig. 11.33 Diagram (a) shows the interaction MO in 1-bromopropane as a base approaches. between the base and the proton, a new C-C The corresponding curly arrow mechanism for

H3Cii

iH

Br 9

between the filled C-H « MO and the vacant C-Br o* The products are shown in (b); a new bond has formed x bond has formed and the bromide ion has been iost. the process is shown below the structures.

the filled C-H o MO and the vacant C-Br o* can be aligned in the same plane, they can have an interaction similar to that between the C-H o MO and the vacantp orbital (see Fig. 11.23 on p. 181).

The interaction between the C-H o 1-bromopropane as a base approaches is mechanism for the reaction is also shown There are three points to note in this

MO and the vacant C-Br o* MO in shown in Fig. 11.33; the curly arrow in the lower part of Fig. 11.33. reaction. The first is the formation of

a new bond between the proton and the base. As we saw before, the hydrogen cannot just fall off by itself as an isolated proton; a base is needed to remove it. In Fig. 11.33 (b) we see the new o bonding MO that has been formed between

the base and the Ht. The formation of this bond is shown in the curly arrow

mechanism by arrow (1). This arrow tells us that a pair of electrons from the base is ultimately going to be bonding the base to the hydrogen.

The second point to note is the formation of a new zm bond between the

two central carbon atoms.

We

can understand this as being a result of the

gradual overlap of the filled C-H o MO and the vacant C-Br o* MO in the starting material. The bonding interaction between these two orbitals is shown by the wavy lines in Fig. 11.33 (a). The new z bond that has formed from this interaction is shown in (b). Curly arrow (ii) tells us two things: that electron

density is moving from the C-H bond as it is breaking and that it builds up in between the carbons forming the new z bond.

The final point to note is the breaking of the C-Br bond. We could think of this as arising from the electrons from the C-H o bond moving into the anti-bonding C—Br o* orbital. As we saw in Chapter 5, filling an anti-bonding MO cancels out the effects of a filled bonding MO. So the interaction between

11.5 (a)

E2 elimination

187

B-H bond partially formed (-)

By

C-H bond

a

partially broken

H t

H

Howe ©, H

*%

C-C x bond

partially formed

Br? C-Br bond partially broken

Fig. 11.34 The transition state of the reaction between 1-bromopropane and a base is shown in (a). The new base—proton and C-C m bonds have partially formed and the old C-H and C—Br bonds have partially broken.

Charge is beginning to develop on the bromine atom and is being lost from the base.

Diagram (b) shows a delocalized MO for a transition state analogous to that shown in (a). This shows that electron density is spread over the whole

with the orbitals in Fig. 11.33.

molecule.

Its shape can be understood

by comparing

the C-H o bonding MO and the C—Br o” simultaneously forms a new C-C x

bond and breaks the C—Br bond. The breaking of the C—Br bond is represented

by curly arrow (iii) which tells us that the electrons from this bond end up on the bromide ion as a lone pair, as shown in (b). The important point is that these three steps are all occurring at the same time. The mechanism is said to be concerted. Fig. 11.34 (a) shows a transition

state for this process. It shows the new bond forming between the base and the proton, the C-H bond beginning to break, the C-C a bond forming and the

C-Br bond beginning to break. The negative charge that was initially on the base is being spread over the whole molecule — still partially on the base but

also beginning to form on the bromide. The full MO picture for this reaction is rather involved but the HOMO for the transition state is rather revealing and is shown in Fig. 11.34 (b). This is

one, delocalized, MO which can hold just two electrons. It clearly shows that electrons are being transferred from the base to the bromide leaving group with

the form of the orbital resembling the interactions shown in Fig. 11.33.

Elimination kinetics Since this elimination mechanism

involves the base and the halogenoalkane

coming together in a single encounter, it should not surprise us that this reaction rate is first order with respect to the concentrations of both the base and the halogenoalkane, i.e. second order overall: rate of elimination = k[1-bromopropane]|[base].

This mechanism is known as an ‘E2’ mechanism, i.e. an Elimination reaction in which the rate-determining step involves two species i.e. is bimolecular. The first elimination mechanism we saw in- Section 11.3, where the bromide ion first fell off the t-butyl bromide to leave the relatively stable trimethylcar-

benium ion which was then quickly attacked by the base, would be termed an

188

Substitution and elimination reactions ‘El’ mechanism. Like the Syl mechanism, this is a first-order reaction since the rate-determining step, the initial loss of the bromide ion, involves only the t-butyl bromide. The El and E2 mechanisms are really the extremes of a continuum of possibilities. In the El, the halide or other leaving group leaves first before the proton is abstracted. In the E2 mechanism, both events happen together, so in

the transition state the halide ion has partly left and the proton has partly been abstracted. If the halide is nearer ‘to having left than the proton is, then the reaction is beginning to look more E1-like. A pure E!] mechanism is rather less common than the E2. An elimination reaction will only take place by an El mechanism if a relatively stable cation can form following the loss of the leaving group and if the base that is present is not too powerful.

If the base is strong, it will get involved and help the

hydrogen come off before the leaving group gets a chance to fall off by itself.

12

The effects of the solvent

Up to now we have neglected a crucial component of reactions — the solvent.

Almost all reactions are carried out in solution, including all the ones going

on in our bodies, but it is all too easy to overlook how much the solvent influences reactions. A good example is the reaction of t-butyl chloride shown in

Fig. 12.1. As was discussed in Chapter 11, this molecule reacts by first forming the carbenium ion (CH3)3Ct

which then goes on to react with either a nucle-

ophile to form a substitution product, or with a base to form the elimination

product, isobutene.

CH,

|

.

.

substitution CHs

Hoc we

|

not CP

N iC} a

CH,

rate determining

sep

3

-

o/

gc“

CH3

cl

u

H

SY

cue,

H3C

7

Nu

0 -H

@

elimination

H3C

H3C

_

_

7 C=

CH

Fig. 12.1 t-butyl chloride reacts first by forming the carbenium ion and then forming either the substitution product or the elimination product. In each case, the rate-determining step for the reaction is the initial formation of the carbenium ion. '

The rate of formation of either the substitution or elimination product de-

pends only on the rate of the initial step in which the carbenium ion is formed; the reaction is therefore first-order. The table below gives values of this firstorder rate constant, k;, at 298 K for the reaction of t-buty! chloride in a number of different solvents. The table also gives the half-life, ty, , of the reaction which is the time needed for the reactant concentration to halve.

ky/s7! ty

water

ethanol

acetone

benzene

pentane

29x 1072

8.5x 1078

13x 107!

69x 10733

10~!6

24 sec

94 days

169 years

30000 years

220 million years

The table shows that whilst the reaction of f-butyl chloride in water proceeds quickly with half of the reagent being used up in 24 seconds, the reaction

in pentane is so slow that it essentially does not occur at all. Even changing the solvent from water to ethanol results in a considerable change in the rate. It is clear that the solvent has an enormous effect on the rate of this reaction. The reaction between CH3Br and Cl, shown in Fig. 12.2, proceeds by the Sn2 mechanism and it is found that the influence of the solvent on the rate of this reaction is opposite to the case of t-butyl chloride. For example, changing

the solvent from water to propanone (acetone) results in a 10? fold increase in

the rate. Moving to the gas phase, where there is no solvent at all, results in a rate increase by a factor of 10!5,

The effects of the solvent

190

a® Vi

H"'y CL}

¢

~Br

OO

Cll LH C

42

Br

(o}

Fig. 12.2 The substitution reaction between bromomethane and chloride ion proceeds 1 04 times faster in propanone (acetone) than water, and 1015 times faster when no solvent is present at all.

A further example of the importance of the solvent is the solubility of one substance in another. Solid NaCl dissolves in water but not in hexane, whereas

the reverse is true for a substance such as naphthalene (Fig. 12.3). We attribute

the ready solubility of ionic compounds such as NaCl in water as being due to

Fig. 12.3 The structure of the aromatic hydrocarbon naphthalene. At room temperature it is a white solid which sublimes readily giving off a vapour which repels many insects — hence the use of naphthalene in moth balls.

the ability of water to solvate ions — something which hexane is very much less effective at doing.

The rate-determining step of the reaction of t-butyl chloride involves the

formation of ions. The fact that the reaction goes so much faster in water than

in pentane is clearly related to the excellent solvation of ions by water. In order to appreciate fully how the solvent can affect the reaction we first

need to understand the nature of the different solvents and how they can interact

with ions.

It is to this topic that the next few sections are devoted and then,

towards the end of the chapter, we will return to answer the question as to why the solvent has such a large influence on the rate of a reaction.

12.1

Different types of solvent

Solvents may usefully be classified according to how polar they are, but trying to quantify this is not particularly straightforward. A useful measure is the relative permittivity (or dielectric constant) of the solvent. In Section 3.2 on p. 21 we saw that the attractive force between two oppositely charged ions with charges c+ and z_ varies with the separation between the two ions, r, according to: Z4z_e7

force = ———~

4reqr2

where e is the charge on the electron (the fundamental unit of charge) and éo is

the vacuum permittivity. In a solvent, the force between the two ions is reduced by a factor called the relative permittivity, €,, of the medium: 4

force =

Z4z—-e*

4megérr

5

(12.1)

Thus, moving to a solvent with a larger relative permittivity decreases the in-

teraction between the ions, as is illustrated schematically in Fig. 12.4. Typical values of ¢, are around 2 for hydrocarbon solvents such as hexane to over 100 for primary and secondary amides. Water — the solvent used in

nature — has a relative permittivity of 80. Solvents with a relative permittivity greater than about 15 are usually described as polar whereas those with smaller values of the relative permittivity

are described as non-polar or apolar. As we shall see, polar solvents are much better at dissolving ionic salts than are non-polar solvents.

12.1

Different types of solvent

(a)

191

(b)

|

(Cc) —_—_—>—

|

reaction coordinate

Fig. 12.22 The energy profile for the reaction between chloride ion and bromomethane in a polar aprotic solvent is shown by the solid line and for the same reaction in a protic solvent by the dotted line. In the protic solvent the free chloride ion is more strongly solvated than the transition state due to the charge dispersal in the latter. The result is that on moving to a protic solvent the energy of the transition state is lowered by less than is the energy of the chloride ion. Therefore the activation energy for the substitution reaction is greater in the protic solvent than in the aprotic solvent.

13

Leaving groups

In earlier chapters we have looked at a number of simple reactions, such as that between ethanoyl chloride and hydroxide, shown in Fig. 13.1 (a), and the formation of a carbenium ion from t-butyl bromide, Fig. 13.1 (b).

(a)

i fe) {ou Hsc~

(b)

OH

O Co!

Cl

H3C~

O

_

© Cl

I

[e

HsC~

OH

CH3 | H3C yok

—_—_»

H3C

@ H3C WiC

—CHg

+

H3C

Br

—~,

Products

Fig. 13.1 Two reactions which we have looked at before and which occur readily: (a) the additionelimination reaction between ethanoy! chloride and hydroxide; and (b) the formation of the trimethylcarbenium ion from t-butyl bromide, which is the first step in the Sy1 and E1 mechanisms.

We now want to understand why some other reactions for which we can

write plausible looking mechanisms do not occur. For example, not attack ethanoic acid to form ethanoy] chloride, as shown in This reaction is simply the reverse of that shown in Fig. 13.1 (a), take place. Similarly, the attack on a ketone by Cl” to give an as shown in Fig. 13.2 (b), does not take place, neither does the

why does Cl~ Fig. 13.2 (a)? but it does not acyl chloride, formation of a

carbenium ion by loss of H~, shown in (c). We know that the same carbenium ion is formed readily by loss of Br~ from t-butyl bromide, so why is it that this ion cannot be formed by loss of H~ from a hydrocarbon?

(a)

O er cl

H3C~ (b)

OH

H3C~

O QL y,

Hac (c)

OP

Cl

I

oe (9H

Eo, 4 Cl

CH

O

nso

(OHS

Hsc~

> .

C

°oH Cl

7oN

CHs |

HCY

no® VI H~

~CHg

HO

—@)

1d) 0 WEDS C H~ ~CHg

(b)

\s

H~

Ho”

H~

O | C

©®

~CH3

~CHg

Fig. 14.2 In (a) hydroxide attacks the carbonyl carbon, simultaneously breaking the C=O x bond to form a tetrahedral intermediate. This intermediate breaks down, as shown in (b), by re-forming the 2 bond and eliminating the only realistic leaving group, which is the hydroxide ion which attacked to form the tetrahedral intermediate in the first place.

Once formed, the only thing the tetrahedral intermediate can do is re-form the ketone by eliminating the only realistic leaving group ~ the hydroxide ion

that just attacked; CH, and H™ are simply not good enough leaving groups to compete with the OH™. The curly arrow description of the collapse of the tetrahedral intermediate is shown in Fig. 14.2 (b).

An equilibrium will be established with both the intermediate and the aldehyde present. For an aldehyde such as ethanal, significant amounts of the in-

14.1

Reactions of carbonyls with hydroxide

217

termediate will be present, but for a ketone, the equilibrium lies very much in favour of the carbonyl. Formation of enolates

The other way the hydroxide could react with the carbonyl compound is as a base; deprotonation leads to an enolate anion of the type shown in Fig. 10.34 on p. 170. The enolate anion formed from ethanal is shown in Fig. 14.3.

enolate anion Fig. 14.3 A strong base may remove one of the hydrogens from the methyl group in ethanal to form an enolate anion. This can be drawn with the charge on either carbon or oxygen; the best representation

is probably that with the charge on the more electronegative oxygen.

We shall now look more closely to see why hydroxide can do this. What we will find is that the C-H bonds on the carbon adjacent to the carbonyl are

weakened as a result of interaction between their orbitals and the m system. This, combined with the fact that the negative charge on the enolate can be

delocalized on to oxygen, results in these hydrogens being significantly more

acidic than in simple alkanes. We saw on p. 160 that in an amide there is an interaction between the nitrogen 2p orbital and the C=O 7 system which leads to the formation of z

MOs which are delocalized over the carbon, nitrogen and oxygen. The ‘lone pair’ on nitrogen is not, therefore, localized on that atom; rather, it participates in a delocalized system (see Fig. 10.18 on p. 161). In an analogous fashion, whilst we might like to think of the C-H and C=O

mz bonds in ethanal as being separate, the computed MOs show there is some degree of interaction between the C—H o bonding orbitals of the methyl group and the a system. Figure 14.4 (a)(i) shows a surface plot of a x MO which contributes to the bonding between the carbon and hydrogens in the CH3 group

in ethanal. The MO may be thought of as arising from an interaction between

the methyl carbon 2p AO and the 1s AOs of the hydrogens above and below

the plane of the o-framework; this interaction is illustrated in Fig. 14.5.

Figure 14.4 (a)(ii) is a surface plot of the same MO but at a lower value of the wavefunction than in (a)(i). Whilst (a)(i) shows that this MO has most electron density on the methy! carbon and the attached hydrogens, (a)(i1) shows

that electron density is also, to a lesser extent, delocalized over the 2 system. Similarly, Fig. 14.4 (b)(i) shows the C=O mw bonding MO resulting from the in-phase combination of the C and O 2p AOs. As usual, there is a greater contribution to this MO from the oxygen AO than from the carbon AO. However, there is also a small contribution from the C-H o bonding MOs on the methyl carbon, as shown in Fig. 14.4 (b)(ii) which is plotted at a lower value

of the wavefunction.

The x* anti-bonding MO,

shown

in Fig.

14.4 (c)(i), is made up largely

from the out-of-phase combination of the C and O 2p AOs, with a greater contribution from the carbon than the oxygen.

As can be seen from (c)(ii),

Competing reactions

218 (a)(1)

(a)(Il)

Fig. 14.4 Surface plots of the 1 MOs of ethanal, i.e. the orbitals for which the plane of the molecule is a nodal plane. The plots in the upper half of the figure are made for a higher value of the wavefunction than those in the lower half. Thus the plots in the upper half just show where the electron density is most concentrated, whereas those in the lower half show the atoms on which smaller amounts of electron density are found. Orbital (a) essentially just contributes to the bonding between the methyl carbon and its attached hydrogens. Orbital (b) is essentially the C=O x bonding MO and (c) is the 1* anti-bonding MO. All the orbitals are to some extent delocalized over the oxygen atom, both carbon atoms and the two out-of-plane hydrogen atoms.

even this MO has a small contribution from the C-H o bonding MOs.

What these three MOs tell us is that there is some weak o conjugation

C 2p

AO

™

A)

ae two

H>_ 2 eG mcr »

O

H

aa

H

1s AOs

Flg. 14.5 The p orbital on the methyl carbon can contribute to the bonding of the methyl hydrogens by overlapping with the 1s orbitals on the two out-of-plane

hydrogens.

electron

the o orbitals for this bond lie in the plane and so are not able to interact with

the x system. In contrast, the orbitals from the C-H bonds of the methy] group lie out of the plane so that interaction with the 2 system is possible. The effect of this o conjugation is that some electron density is withdrawn from the methyl C—H bonds towards the oxygen. This weakens the bonds and

makes the hydrogens more acidic than they would be in a simple alkane. We

saw a similar example on p. 179 where neighbouring C-H o bonds helped to stabilize a carbenium ion. We also saw how the resulting withdrawal of

electrons from the C-H bonds made the hydrogens sufficiently acidic that they

density

pulled towards O

OOD

between the C-H o bonding MOs of the methy] group and the z system; this is shown schematically in Fig. 14.6. Note that this conjugation is not possible for the C-H bond between the carbonyl carbon and the attached hydrogen as

oe

could be removed by a base, such as hydroxide, and how this led to elimination

(2 ¥

out-of-plane C-H —H oo orbita orbital

p orbitals on C and O Fig. 14.6 The C-H o bonding MOs of the methyl group and the 2p orbitals on the

carbonyl carbon and the oxygen can ali interact to form a delocalized set of MOs. Note that for this interaction to be successful the C—-H bonds must lie out of the plane of the molecule. Electron density is pulled towards the oxygen due to its greater effective nuclear charge.

reactions (see Section 11.3 on p. 180).

In ethanal, this o cgnjugation increases the acidity of the hydrogens attached to the carbon adjacent to the carbonyl]. In addition, the enolate anion which results from the removal by a base of one of these hydrogens is delocalized. Taken together, these two effects account for the fact that it is much

easier to remove H* from either an aldehyde or a ketone than from a simple

alkane. Typically, these carbonyl compounds have pK, values of around 20, in contrast to simple alkanes which have values of between 40 and 50.

Figure 14.7 shows two curly arrow descriptions of the formation of an enolate. Although both mechanisms are acceptable, (b) is preferred since it em-

phasizes the role of the C=O bond withdrawing electrons from the C-H bond,

making the hydrogen acidic in the first place. Also, as we saw in Fig. 10.34 on p. 170, when representing the enolate ion it is better to have the negative charge

14.1

Reactions of carbonyls with hydroxide

oF

aowcal ,,

io

Y*,

==

219

He

i

Not e

|

+

HO

+

H50

H

HO

(b)

CO

"9

7 Cc ~c~ H

%

— ~

H

«=> Cc So

|

H

Fig. 14.7 Two curly-arrow representations of the formation of an enolate. Version (a) shows the deprotonation by hydroxide ion to form the enolate; this version does not emphasize the electron-withdrawing nature of the C=O bond which is what makes the hydrogen acidic in the first place. The effect of the carbonyl is represented in version (b); in addition, this also suggests the enolate formed has a greater charge on the oxygen than on the carbon.

on the more electronegative oxygen atom.

However, the structure which has

the charge on the carbon does make a contribution, so we should think of the

enolate as having significant charge on both the oxygen and the carbon. In summary there are two possible reactions that could occur between hydroxide and ethanal: the first is the direct attack of the hydroxide into the 7*

MO of the ethanal to form the tetrahedral intermediate; the second is the de-

protonation of one of the methyl hydrogens to form the enolate. The question is, which reaction actually occurs? The answer to this is simple: they both do. Both of these reactions are reversible so at any one time the reaction mixture will contain the unreacted hydroxide and aldehyde, the tetrahedral intermediate and the enolate. We shall see later that there may also be further reaction products.

How do we know that both reactions are occurring?

Experimental evi-

dence for this comes from studies using isotopically labelled reagents, details of which are given in the next section.

Isotopic labelling It is possible to prepare water or hydroxide where the normal 160 atoms or hy-

drogen atoms are replaced with their heavier isotopes !80 and deuterium (D or

2H), When !8Q-labelled hydroxide and water are mixed with '6Q-containing

aldehydes and ketones, it is found that the heavier oxygen isotope is readily in-

corporated into the carbonyl compounds. The mechanism by which this occurs

in shown in Fig. 14.8. Similarly, if deuterated water (D2O) and deuteroxide (OD~ ) are used, the

methyl hydrogens are rapidly exchanged for deuterium atoms. The mechanism for this reaction is shown in Fig. 14.9.

Competing reactions

220

h eu" 18

H

129% \|

_@ ~

Ws

H~ ~CHs 4

H~

H

H~

~CHg H

06>

Cc

:

oH

H

TON —H

NS

a’

CHs

H* 109%) 9-H

oO.

~CHs

oH).

18

fo)

H~

189

9.

~CHs

H~

|

20

NX

~CHs

Fig. 14.8 Illustration of how '80 from '8OH- can be incorporated into carbonyl compounds.

Step

(a) shows the initial attack of the labelled hydroxide on the ethanal. The best leaving group after this step is still the labelled hydroxide that just attacked — we need to make the unlabelled oxygen into the best leaving group. In water, there is extensive hydrogen bonding between the solvent and any -O— ions; this aids the tetrahedral intermediate in protonating the -O~ and deprotonating the OH group. Thus step (b) shows the intermediate deprotonating the solvent and (c) shows the labelled hydroxide deprotonating the other OH group. The net effect of these two steps is that the unlabelled oxygen now becomes the better leaving group (as OH ) and is then pushed off in step (d) by the O~ to yield the

180-labelled product. All of the steps are reversible, so given the large excess of '80-labelled water

and hydroxide, eventually almost all of the initial 160 in the ethanal will be replaced.

C

D~